scSplit: Bringing Severity Cognizance to Image Decomposition in Fluorescence Microscopy
Authors: Ashesh
Florian Jug
Venue: NeurIPS 2025 poster ()
Keywords: semantic unmixing
image decomposition
Fluorescence microscopy
Computer vision
inverse problem
Primary area: machine_learning_for_sciences
TL;DR: We propose a novel network architecture capable of decomposing mixed fluorescence microscopy images (input = wA + (1-w)B ) into their constituent components (A and B) across a wide range of mixing ratios (w ∈ (0.1,0.9)).

Abstract: Fluorescence microscopy, while being a key driver for progress in the life sciences, is also subject to technical limitations. To overcome them, computational multiplexing techniques have recently been proposed, which allow multiple cellular structures to be captured in a single image and later be unmixed. Existing image decomposition methods are trained on a set of superimposed input images and the respective unmixed target images. It is critical to note that the relative strength (mixing ratio) of the superimposed images for a given input is a priori unknown. However, existing methods are trained on a fixed intensity ratio of superimposed inputs, making them not cognizant of the range of relative intensities that can occur in fluorescence microscopy. In this work, we propose a novel method called scSplit that is cognizant of the severity of the above-mentioned mixing ratio. Our idea is based on InDI, a popular iterative method for image restoration, and an ideal starting point to embrace the unknown mixing ratio in any given input. We introduce (i) a suitably trained regressor network that predicts the degradation level (mixing asymmetry) of a given input image and (ii) a degradation-specific normalization module, enabling degradation-aware inference across all mixing ratios. We show that this method solves two relevant tasks in fluorescence microscopy, namely image splitting and bleedthrough removal, and empirically demonstrate the applicability of scSplit on 5 public datasets. The source code with pre-trained models is hosted at https://github.com/juglab/scSplit/.

scSplit:
Bringing Severity Cognizance to
Image Decomposition in Fluorescence Microscopy
Ashesh Ashesh Human Technopole ashesh wsw.saaatt..s...ooo...
Florian Jug Human Technopole florian. juge . org
Abstract
Fluorescence microscopy, while heing key driver for progress in the life sciences, is also subject to technical limitations. To overcome them, computational mul- tiplexing techniques have recently been proposed, which allow multiple cellular structures to be captured in a single image and later be unmixed. Existing image decomposition methods respective unmixed target images. It is critical to note that the relative strength (mixing ratio) of the superimposed images for a given input is priori unknown. However, existing methods are trained on fixed intensity ratio of superimposed inputs, making them not cognizant of the range of relative intensities that can occur in fluorescence microscopy. In this work, we propose novel method called scSplit that cognizant of the severity of the above-mentiones mixing ratio. Our idea is based on InDI, popular iterative method for image restoration, and an ideal starting point to embrace the unknown mixing ratio in any given input. We introduce (i) suitably trained regressor network that predicts the degradation level (mixing ratio) of given input image and (ii) degradation-speecie malization module, enabling degradation-ave -aware aware inference across all mixing ratios.
trained on of superimposed input images and the
nor-
We show that this method solves two relevant tasks in fluorescence microscopy, namely image splitting and bleedthrough removal, and empirically demonstrate the applicability of scăplit on public datasets. The source code with pre-trained models is hosted httpt::::///.......t.m / thub. wtt. sttpb//ccspptt///cc
Introduction
Fluorescence microscopy is widely utilized imaging technique in the life sciences, enabling researchers to visualize specific cellular and subcellular structures with high specificity. It employs distinct fluorescent markers target different components, which are subsequently captured in separate image channels. The global fluorescence microscopy market, valued at 9.83S billion in 2023, projected to expand significantly in the coming years, reflecting its critical role in advancing biological research [
Still, there practical limitations the maximum number of structures that be imaged in one sample. To mitigate this, the idea of imaging multiple structures into single image channel has recently been gaining popularity 2 3. In such approaches, the image produced by the microscope is a superposition multiple structures, and a deep-learning-ber bbased setup then used to perform the image decomposition task, thereby yielding the constituent structures present in the superimposed input as separate images.
While these approaches have been beneficial, they have not explicitly addressed particular aspect of this problem. The relative intensity of the superimposed structures in the input can vary significantly depending sample properties, labeling densities, and microscope configuration. For instance, in a superimposed image of nuclei and mitochondria, nuclei may be dominant in their intensities,
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Training
Inference
t ~ P(t)
co
C1
1.
Cj (1 - t)co0 + tc
{t1: 82g 3.. Eugg
Looss
Norma Eowionziion Ezwion Module
2.
GO
Superimoosed Input
do +
Gi
tass
Gemp
Gen
(Loss)
bayer
c1
Rlgg
Precictoons
Figure 1: Schematic overview of the scSplit framework for handling image superposition varying severity levels. (Left) Training pipeline: The input to the system is superimposed image, generated as a weighted average of two images using mixing ratio t E [0, 1]. The superimposed image is passed through normalization module, which performs ratio-specific normalization ensure mean and unit standard deviation. The normalized image then processed by two generative networks, Geno and Gen estimate the individual structures. regressor network, Reg, is trained to predict the mixing ratio from a normalized superimposed image. (Right) Inference pipeline: During inference, the mixing ratio is estimated for set of superimposed input images using Reg, and the estimates are aggregated to obtain tags- The normalized superimposed images, along with bagg fed into the generative networks Gen; to recover the individual structures. Thanks the mixing-ratio specific normalization during training, the normalization during inference simple and performed using the mean and standard deviation computed from the set of test input patches.
with the mitochondria showing as relatively faint structures. Existing methods, which are not cognizant of such variations in superposition severity, exhibit performance degradation when applied to images with superposition characteristics different from those encountered during training. We highlight the significance of this issue of severity cognizance by noting that a related problem, known Bleedthrough, exists in fluorescence microscopy. When imaging biological structure into dedicated channel, other structures can become visible due to insufficiently precise optical filtering. In such cases, say that this other structure "bleeds through" into the currently imaged channel. See Sup. Fig. for pictorial description of the task at hand. Note, only if the challenge of relative intensity variation is effectively addressed will single network ever be able to effectively solve both the image unmixing task and the bleedthrough removal task.
To address this, we propose scSplit, method that incorporates the desired cognizance about the superposition severity directly into the inductive bias of the method itself. We leverage the inductive bias embedded in the training methodology of InDI 44, popular image restoration method. For a given superimposed input containing structures A and B, scSplit first explicitly predicts a mixing ratio t [0, 1]. which quantifies the severity of the superposition, with t = 0 meaning that only A is visible the input, while / = 1 conversely meaning that only structure B can be seen. scSplit then uses the estimated mixing ratio along with the superimposed input to predict estimates of A and B. To ensure that the network remains in-distribution for superimposed images with varying superposition severities, we introduce Severity Cognizant Input Normalization (SCIN) module. This module not only addresses the normalization requirements but also simplifies the inference process, as we show in Section 3 Additionally, leveraging domain-specifie knowledge from fluorescence microscopy, we incorporate an aggregation module that enhances the accuracy of the mixing ratio estimation during inference. By integrating these advancements into scSplit, we introduce method designed to simultaneously address two critical tasks in fluorescence microscopy image unmixing and bleedthrough removal-by being cognizant of the severity of the superposition.
2 Related Work
In the field of fluorescence microscopy, image decomposition techniques have recently gained signifi- cant attention for addressing the image unmixing problem. Seo et al. (5) introduced a linear unmixing approach to separate l structures, which, however, necessitates A input channels, each representing

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distinct superposition of the k structures. More recently, deep learning based frameworks have emerged 3 2 6 capable of predicting individual structures from a single image channel. Ashesh et al. (3] proposed GPU-efficient meta- meta-architecture, seSplit, which leverages contextual information from surrounding regions of the input patch. HVAE [79] and U-Net [10] were used as the underlying architecture for saSplit. Three variants of µSplit were developed, each optimizing trade-off between GPU utilization and performance. Further advancements were made with denoiSplit [Л]] which combines unsupervised denoising with supervised image unmixing. More recently MicroSplit [6] combined the GPU efficiency of yuSplit with unsupervised denoising, sampling, and calibration of denoiSplit. It also provided several image unmixing datasets containing real microscopy images of different structure types. However, existing single-chamnn input methods [3] [ typically assume the input to be an average of the two structures, thereby overlooking the variability in superposition inten- sity present in real-world microscopy images. While the MicroSplit analysis successfully quantified the effects of superposition variability, it did not extend proposing resolution. This highlights the need for more robust approaches to handle the complexities of real imaging data.
Next, we situate the image unmixing task within the broader context of Computer Vision. Image unmixing can be viewed as a specialized form of image translation, where the objective is to map an image from a source data distribution to multiple images, each belonging to a specific target data distribution. Over the past decade, the field of image translation has witnessed significant advancements, with a wide array of methodologies being proposed. These include architectures such as U-Net [TO]. generative adversarial networks (GANs) [2-14]] and iterative inference models like diffusion models [15] [6] and flow matching techniques [17119 among others. These approaches have demonstrated remarkable capabilities in addressing various challenges in image-to-image transformation tasks, providing rich foundation for advancing image unmixing techniques.
Iterative models offer the advantage of providing access to intermediate predictions during the inference process. In many such methods, these intermediate predictions-afies accounting for noise-closely resemble a superposition of the source and target data distributions. Consequently, when the degradation process itself involves superposition, as is the case in our task, iterative models emerge as a natural choice for modeling the degradation. Literature suggests that the superposition of structures in fluorescence microscopy can be approximated as linear superposition (20)22) This insight led us to adopt InDI [4, a well-cstablished iterative image restoration method that explicitly models degradation average between the clean target and the degraded input using a scalar mixing ratio to generate a "less" degraded input. The generated input and the mixing ratio are then fed to network as inputs, and the network is trained to predict the clean target. The inductive bias of this training framework aligns precisely with the linear superposition observed in fluorescence microscopy, making InDI suitable foundation for our proposed approach.
linear mixing process. In InDI, the idea is to take the weighted
Finally, we observe that within the broader domain of image translation, the task of image unmixing shares similarities with tasks such as reflection removal, dehazing, and deraining (23/26]. However, these tasks differ fundamentally from fluorescence microscopy unmixing in aspects like superposition linearity and ground truth availability. See Sup. Sec. J for more details.
3 Our Method
Here, we begin by establishing the necessary formal notation. Then, we address the limitations of existing normalization schemes when performing inference from intermediate timesteps, and present our improved normalization approach. Finally, we outline the training process, including the loss formulations for the generative networks (Geng and Gen,) and the regressor network (Reg ) as illustrated in Figure
3.1 Problem Definition
Let us denote a set of l: image pairs by C = (G) (ct,c,,,,,, We denote by Co- (cb: . and C = of..c the two sets of images from the two distributions of images we intend to learn to unmix. For brevity and readability, we will omit the superscript unless needed. For a pair of images (cg E Co e E C1) and a mixing ratio t E [0, 1). an input to be unmixed is defined by the wixe linear combination
G (1 -t)co + to
(I)
3

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With this notation at hand, we define the task of Image Decomposition as the computational unmixing of given superimposed image q into estimates én and é1. In this context, we introduced the term superposition severity to describe the dominance of one channel in the superimposed input, which is precisely quantified by the mixing ratio 1.
The assessment of the quality of any solution for the image decomposition task is evaluated by computing the similarity between dg and é₁ the true images ep and c₁, respectively.
3.2 Severity Cognizant Input Normalization (SCIN)
We begin by observing that the normalization procedure for the input patch has not received any special attention in the existing image unmixing works 6), and the standard practice of mean and standard deviation based normalization is performed, where the mean and standard deviation computation is done over the entire training data. With natural images, common normalization strategy is to divide by 255. Such a data-independent normalization is not suitable for Fluorescence microscopy data, which is typically stored in the nint1 data type, since intensity distributions vary significantly depending upon the imaging conditions. For instance, it is common to have the maximum pixel intensity for a noisy acquisition to be less than 200, whereas the pixel intensities can easily be larger than 20000 for less noisy acquisitions.
In InDI 4. where the input also has the same formulation as Eq. I Cy and e1 are separately normalized according to statistics derived from Co and C1, respectively. It is worth noting that similar normalization schemes commonly employed in iterative models in general that operate with two data distributions and have the objective of translating from one distribution to another.
To understand why a more involved normalization module is required, we next provide the expression for the expected mean R[u(t)] and the variance [t)) of random superimposed patch o given a mixing ratio t, with expectation computed over the set of patches c for a given t. Please refer to the Sup. Sec. A for the derivation. Using Eq. one can write Blu(t)] = (1 - [)o + +[E[pi] and
E[o²(0) = - =)² (1-)))=(11)))000000
+ (B)) + 21(1 ----tt(Coo t)Coo(pp.PP).
where po and Pi denotes a random pixel from co and ei respectively and Cov[::] denotes the covariance. One of the default ways to do data normalization is to standardize the sets of images Co and C1 to have zero mean (E[pu] = Eppp] 0) and unit variance [ = E[o² = 1). In this case, one obtains E [[][ = 0 and [[o
t² + (1 (1-11 t)² + 2f(1 - Covo pr). Note that while Elu(t)] is for all f, the expected variance is function of t. We support this claim with empirical evidence in the Sup. Fig. [.119 What this means is that during training. for a given mixing ratio t, the network sees the superimposed patches drawn from a distribution of images having zero mean and standard deviation dependent on f. To get optimal performance on superimposed input during inference, we would want the input image to be suitably normalized so as to have similar statistics. This leads to critical complication when we want to do inference on et with an unknown E [0, 1] using a trained scSplit network. Without knowing t for an input, we cannot normalize correctly.
The solution we propose is to avoid the problem altogether by introducing Severity Cognizant Input Normalization Module (SCIN), ensuring that for every t, E[u((t) = O and ([o² = 1.0. To enable this, we must first empirically evaluate what E[ and E (t)] are for partition of the interval [0, 1]. We split the interval [0. 1] into n 100 equally sized disjoint partitions. We generate n sets of
mixed image patches C. = (ce : i (1_ [1 [O...., n 1] by extracting image patches of fixed size from image sets Co and C₁ and performing pixelwise weighted average as in Equation []] For each input patch in each set, we compute the mean and standard deviation. For each set, we aggregate these values to get the expected mean and standard deviation and store them in a list of tuples D. such that D[i] = o:). After creating a superimposed image patch e as described in Eq. [ during training, we standardize o, for all < 1 using the mean and variance saved in D[ (n J.. The normalization module we propose simplifies inference by decoupling input normalization from the mixing ratio. During training, we enforce [[](()] 0 and (l) = 1 across all mixing ratios. During inference, test inputs from a single acquisition can therefore be normalized using the mean and variance computed directly from the images in that acquisition.

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3.3 Network Setup
Similar to InDI 4 we use Gaussian noise perturbation on the input. Let Let denote the normalized Ct, with normalization done described above. Input to the network becomes X, Cx c2omm + len, with n (O, 7) and 6 = 0.01.
Generative Network Gen, We use two generative networks, Geny and Geng, to give us estimates of c0 and efam respectively. As shown in Figure [ they take as input the normalized superimposed image along with an estimate of the mixing ratio, which represents the severity of the unmixing to be done. Unmixed prediction for the channel i E {0, } can be expressed as 2 = Gen, (x,, td; (1 - ()61-e), where & denotes Dirac delta. Note that the severity of the unmixing for estimating co and C₁ is f. and 1 t, respectively.
Regressor Network Reg to Estimate the Right Mixing Ratio. Our regression network Reg predicts an estimate of the mixing ratio i given input Fy, which then used by Gen; networks during inference. Crucially, Reg incorporates the same normalization module proposed for the Gen, networks (Section 3.2) and the reasons are identical. As seen before, the normalization statistics for Ta are inherently dependent on f. During inference, inputs must be normalized using statistics consistent with their true to avoid distributional mismatch. This creates a cyclic dependency: accurate regression of t requires proper normalization, but normalization requires the knowledge of t. Resolving this interdependence central to our framework's 's design.
Next, we utilize domain knowledge to further improve our estimations of L. We know that for all images acquired during a single session at microscope, the same laser power settings and the same fluorophore types will be used. This means that the mixing ratio of all these images can be assumed to be the same. Hence, we aggregate the values estimated from the set of images belonging to single session and use that during inference. The aggregation is implemented as simple arithmetic mean of the values obtained for individual images the session, In the Sup. Sec. H we experiment with different aggregation methods.
Distribution for p(t). During training, we sample the mixing ratio & from distribution p(t). To model p(t), we modify the distribution denoted 'linear,' in InDI, adapting it to
1 U10, 1] 1+a do.5.
p(t)
with a = 1 in all our experiments. Unlike InDI, where more weight was given via the Dirac delta distribution to 1, we need more weight on t = 0.5. This is because the image unmixing task involves inputs containing both structures, making it more appropriate to assign a higher weight to t= 0.5 rather than / = 1.
4 Results
In all qualitative figures and tables. we define the input as x., w O-wanted + (1 w) * Ch This notation allows us to relate directly to the strength of the channel we are evaluating. The value of w determines the nature of the prediction task. When w 0.1, the objective is to predict the dim structure within the superimposed input. Conversely, when w 0.9, the task shifts to identifying and removing the dim structure, effectively isolating the dominant structure. This latter scenario is commonly referred to as the bleed-through removal task in the field.
Datasets and Unmixing Tasks, We tackle five tasks coming from five real microscopy datasets, namely Hagen al. (29), BioSR (30), HTT24 6 HTLIF24 (6, and PaviaATN [.] From the BioSR dataset, we tackle the ER vs. Microtubules task. From the Hagen et al., we tackle the Actin vs. Mitochondria task. Following puSpit B3 we clip pixel values at 1993.0 for this dataset to have fair comparison. From HTT24, we tackle the SOX2 vs. Golgi task. From HTLIF24, we choose the Microtubules vs. Centromere task and from PaviaATN the Actin vs. Tubulin task. The HTT24 and HTLIIF24 datasets also include microscope-imaged superimposed inputs, which we additionally evaluate. Using the laser power ratios employed for the two structures in these datasets as a proxy for mixing ratio, we obtain 0.5 and 0.41 for HTT24 and HTLIF24, respectively.
5

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Dataset
Dominant
Balanced
Weak
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
Iop vs Tar
34.1
0.973
0.047
25.1
0.889
0.148
21.2
0.784
0.243
U-Net
31.8
0.965
0.063
28.2
0.921
0.122
22.0
0.833
0.222
aSplit,
33.7
0.965
0.048
31.9
0.961
0.067
23.2
0.857
0.167
pSplit x
33,9
0.962
0.046
32,4
23.6
0.858
0.165
Hagen
pSplitp
33.1
0.967
0.045
32.4
0.964
0.058
23.4
0.863
0.158
al
denoiSplit
32.4
0.958
0.166
31.9
0.954
0.169
23.1
0.851
0.246
MicroSplit
34.7
0.957
0.167
31.7
0.956
0.168
25.0
0.862
0.240
InDI
33.1
0.963
0.043
32.1
0.965
0.052
24.2
0.879
0.138
scSplitu.s
34.1
0.979
0.012
33.7
0.975
0.145
25.0
0.881
0.141
scSplit
40.6
0.994
0.011
33.3
0.976
0.046
28.0
0.929
0.123
scSplit
40.9
0.994
0.011
33,9
0.977
0.046
29.3
0.934
0.123
Inp vs Tar
42.3
0.989
0.018
33.3
0.075
29.5
0.881
0.139
U-Net
45.9
0.980
0.023
44.6
0.986
0.016
36.0
0.939
0.066
uSplit
46.7
0.978
0.024
45.1
0.986
0.016
36.6
0.940
0.068
pSplit x
0.978
0.024
36.5
0.940
0.068
"Split
45.9
0.979
0.024
44,9
0.986
0.016
36.4
0.942
0.066
HTLIF24
denoiSplit
44.8
0.981
0.029
42.9
0.985
0.025
35.8
0.938
0.075
MicroSplit
45.0
0.982
0.029
43.7
0.986
0.025
36.5
0.939
0.073
InDI
45.2
0.976
0.031
43,9
0.991
0.012
37.6
0.963
0.055
scSplitu.s
45.9
0.987
0.015
45.1
0.991
0.013
37.4
0.951
0.065
scSplit
50.1
0.997
0.003
44.0
0.993
0.010
38.8
0.975
0.035
scSplit
51.8
0.998
0.002
45.5
0.994
0,009
39.9
0.976
0.034
Inp vs Tar
33,9
0.937
0.119
24.1
0.746
0.311
21.1
0.504
0.498
U-Net
37.2
0.924
0.066
33,7
0.958
0.059
25.6
0.740
0.292
aSplit,
37.8
0.918
0.066
33.5
0.959
0.051
25.7
0.738
0.291
pSplitz
37.8
0.921
0.060
33,0
0.960
0.049
25.7
0.748
0.276
uSplit
37.5
0.915
0.070
32,6
0.956
0.059
25.2
0.744
0.278
BisSR
denoiSplit
36.4
0.929
0.083
33.1
0.957
0.086
25.3
0.733
0.322
SicroSplit
38.5
0.932
0.068
34.3
0.966
0.065
26.6
0.759
0.274
InDI
35.9
0.917
0.054
33.4
0.953
0.050
26.3
0.802
0,211
scSplito.s
37.3
0.957
0.033
35.0
0.967
0.037
26.4
0.770
0.236
Scspii
39.3
0.986
0.012
33.7
0.965
0.039
27.2
0.868
0.153
scSplit
40.1
0.987
0.011
35.3
0.973
0.033
28.7
0.889
0.130
Iap Tar
38.7
0.978
0.013
29.6
0.300
0.075
25.8
0.783
0.149
U-Net
37.9
0.963
0.042
37,5
0.965
0.020
30.1
0.883
0.059
aSplit,
37.3
0.953
0.046
36.6
0.959
0.021
29.7
0.880
0.059
pSplit x
37.6
0.954
0.046
36.9
0.959
0.021
29.9
0.880
0.059
HTT24
aSplit
37.5
0.954
0.045
36.8
0.960
0.021
29.8
0.880
0.059
denoiSplit
37.3
0.954
0.055
37.5
0.964
0.028
31.0
0.896
0.062
MicroSplit
36.9
0.950
0.061
36.6
0.959
0.032
30.3
0.891
0.063
InDI
37.6
0.962
0.034
36.5
0.966
0.017
30.5
0.909
0.057
s:Splifa.s
38,1
0.984
0.018
38.6
0.008
31.4
0.902
0.063
scsplit..... agg
43.4
0.993
0.002
38.2
0.979
0.007
33.7
0.939
0.030
scSppii
44.5
0.995
0.001
39.1
0.981
0.0055
34.7
0.943
0.028
Tar
31.0
0.932
0.104
22.3
0.754
0.294
18.2
0.548
0.480
U-Net
29.3
0.870
0,210
25.4
0.743
0.346
21.2
0.568
0.500
sSplit,
27.0
0.889
0.133
24.3
0.780
0.241
21.1
0.622
0.396
pSplit g
27.4
0.905
0.120
24.7
0.800
0.228
21.1
0.639
0.387
uSplit,
27.9
0.908
0.127
25.2
0.808
0.241
21.3
0.648
0.399
PavinATN
denoiSplit
27.3
0.857
0.772
26.2
0.843
0.794
21.8
0.750
0.824
MicroSplit
24.0
0.771
0.896
21.8
0.688
0.952
18.8
0.540
1.000
InDI
29.9
0.943
0.131
23.9
0.858
0.192
21.7
0.741
0,248
scSpli 0.6
29.0
0.948
0.082
27.1
0.135
21.2
0.774
0.226
scSplit.....
33.9
0.976
0.035
27.1
0.903
0,166
23.9
0.819
0.387
scSplit
33.1
0.977
0.033
27.6
0.907
0.155
24.3
0.823
0.377
Table 1: Quantitative evaluation of unmixing performance across five tasks. We categorize the input into three regimes based on the dominance of the target channel: dominant (w E [0.9, 0.8, 0.7}). balanced (w {0.6, 0.5, 0.4)). and weak (w {0.3, 0.2, 0.11). The reported metric values are averaged across both channels and all values of w within each regime. To account for the varying difficulty of the regimes, we include a comparison between the input and the target in the first row for cach datasct. Metrics include Multiscale SSIM (MS-SSIM) (27 and range-invariant PSNR (28) The grayed and underlined entries indicate the best and sccond- best results for each metric, respectively.

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Inpul (c 0.9)
Splii P
denuiSplitt
InDi
scSpli
Targei
PARE
HAME
PUSE
PSMR 35.3
PSRR 10.
PS4R 20.0
PO93 22.3
Input (uo 0.8)
j+ppitt
denoilipiit
InDT
scSipiir
Target
Figure 2: Qualitative evaluation of unmixing performance. We show qualitative evaluation Hagen [29] (top panel) and BioSR [30) (bottom panel). For each dataset, full input frame (top-left) and zoomed-in input patch (bottom-left) are displayed. Predictions and corresponding targets (last column) are for the input patch. They are shown for both channels, with cach channel displayed in a separate row. PSNR values are also reported for the predicted patch. The mixing ratio indicated above the input column corresponds to the first channel, with the second channel naturally having ratio of (1 w). Additional qualitative evaluations
across different us values for datasets are provided in Supplementary Figures through
HT-L1F24
HT-T24
Mixing-ratio
PSNR
LPISS
PSNR
SSIM
LPIPS
UNet
(4:1)
30.1
0.906
0.074
lop va Tar
32.9
.947
.193
29.4
.894
.152
denoiSplit
(4:1)
28.8
0.854
0.09
UeN
40.7
.990
.021
35.6
.955
.015
scSplit as
(4:1)
32.3
0.914
0.069
Spllt,
40.6
-990
.022
35.0
949
.017
sclipii (aagg .82)
(4:1)
35.8
0.956
0.020
Spplit
40.9
.991
.021
35.1
.950
.017
UNet
(1:4)
28.5
0.878
0.109
spplit
40.9
.991
02.
35.2
950
.017
denoiSplit
(1:4)
SenoiSplit
39.8
988
.03
36.6
96
.30
sciplit
(1:4)
32.3
0.927
0.067
MicroSplit
40.1
.991
034
35.8
954
031
seSplit (fang 225)
(1:4)
0.955
0.020
InDI
41.2
sclplit,
41.
9991
.016
35.9
955
017
Table 3: Evaluation on superimposed raw mi-
scSpii
35.6
.955
.019
croscopy images exhibiting increased train-test dis- tribution shift. We the HT--224 dataset, with the test set metries identical to those Table How- ever, relative to Table
splp
40.9
.992
.155
36.0
957
.017
Table 2: Evaluation on superimposed raw mi- croscopy images. For the HT-LIF24 and HT-T24 datasets, we evaluate raw superimposed images with roughly balanced channel intensities. The metric 'SSIM' refers MicroMS3IM (3T] Best and second- best results per metric are indicated by grayed and underlined entries, respectively.
training data exhibits substantially different mixing ratio from the test set, resulting in noticeable drop in the performance of the strongest baseline methods. Despite this, scSplit still demonstrates comparatively robust performance in these conditions.
Baselines. As baseline, we use U-NET [10), with the implementation as used in [3]. Next, we use the three architectures proposed in ySplit [3] namely Lean-LC, Regular-LC, and Deep-LC. as baselines which we refer to sdSplit,, SSplit R. and μuplit respectively. For the Hagen et al. [29] and the PaviaATN [3] data, we used publicly available pretrained models for the abovementioned baselines. Next. we use the official implementation of denoiSplit as baseline where we increased patch size (from 128 to 512) to ensure a fair comparison with scSplit. We use the official
implementation of MicroSplit with its default hyperparameters. Finally, we use InDI as baseline. Since there is no available official implementation for InDI, we implemented it. To ensure fair comparison, we utilized the same hyperparameters for both InDI and scSplit implementations. For
7

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Channel: Microtubules
Channel:
40.0
893
40.
32.5
P5NR
35.2
M553
30.0
400.3
M001
22.
20.6
Wassumed
Wassimed
Irput 0.5)
Predictions
Target
0.8
0.5
Wassumed 0.2
Wanner 0.1
Figure Performance evaluation the regressor network Reg (a) Quantitaive evaluation of performance degradation with incorrect w during inference: This analysis highlights the sensitivity to inaccurate predictions by Reg. The x-axis represents the assumed to during inference, the legend represents the actual w, and the y-axis quantifies the performance. (b) Qualitative evaluation on the BioSR dataset with varying during inference: Predictions are shown for each channel (two rows) under different assumed w values. For each w, the input divided into upper lower halves, displayed two sub-rows.
first sub-row sets negative pixel values to zero during visualization, while the second sub-row uses default visualization. It is worth noting that significant artefacts (tiling artifacts, disappearance of structures, and increased "crispness" of microtubule curves) get manifested when the assumed w is reasonably far from 0.8, the value used to create the input.
our InDI baseline, we use = 0.5 during inference and use the p(t) defined Eq. 3 during training. Please refer to the supplement for more details these baselines. To evaluate the models superimposed images directly captured with a microscope, we trained all models with synthetic inputs and used these 'real' inputs for evaluation. To separately showcase the benefits of the Reg network and the aggregation operation, we have two variants scSplit, namely scSplit and scSplit_ additional baselines. scSplito.5 does not the Reg network, and instead always uses / 0.5 during inference. scSplit_ agy uses the Reg network, but does not perform aggregation of estimated Finally, for InDI, scSplit, and all variants of scSplit, we employ one-step inference to minimize distortion. For more detailed discussion on it, please see Sup. Sec. D
Quantitative Evaluation. In Table we present quantitative results. Here, we consider three input regimes, namely 'Dominnn', "Balanced", and 'Weak', each differing from the other on the strength of the structure we are interested in. While the Weak regime, the structure we desire to extract from the input is barely present, the desired structure is dominant in inputs from the 'Dominant' regime. Within the lexicon microscopy, inputs derived from the Strong regime are designated as exhibiting 'bleedthrough' For each regime, we average the performance over the two channels and the 3 different w values as mentioned in Table Please refer to the Sup. Sec. for more details on the evaluation procedures.
From Table I is clear that scSplit does a good job across all input regimes, and especially for Dominant regime, that is, for higher w values. This result shows that single trained scŠplit network, which is cognizant of the severity of superposition, can solve both the bleedthrough removal task and image unmixing task.

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deep-LC
deep-LC + UI0.11
desp-LC + Eq
seppi:
40
Channel
45-
Channel
35
PSNR
30-
02-
(Cs. GJI stparete norm
25-
20
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
Figure Analysis factors contributing the normalization module on the Hagen et al. dataset: The conventional normalization of Go and C1 leads to out-of-distribution issue during test evaluation. In contrast, our u-specific normalization scheme demonstrates superior performance. (Right) Comparison against suitable augmentations: We investigate one key factor behind scSplit's enhanced performance: its exposure inputs with varying levels of mixing during training. this, we introduce two augmentations to input generation process PSplit [], one of our baselines. allowing it to also observe different mixing levels during training. While these augmented ySplit, variants show improved performance over the vanilla pS scăplit consistently outperforms them across mixing ratios w.
superior performance scSplit. (Left) Justification for
As mentioned above, we also have real superimposed images for the balanced regime in the HTT24 and HTLIF24 datasets. We show the quantitative evaluation in Table 2 Although all baseline methods are optimized for the balanced regime and these real input images also belong to that regime, scSplit achieves competitive performance even under these conditions, evidenced by the results in Table 2 To address potential concerns that scSplit may offer limited advantages for real superimposed images, conduct additional experiment the HTT24 dataset to demonstrate its effectiveness. In this experiment, we demonstrate that scSplit outperforms baseline methods when the relative intensities of structures in real superimposed inputs differ from those in synthetic sums. From the HTT24 dataset, we created two variants by multiplying all pixel values in one structural channel by a factor of 4. In the first variant, the first channel is brighter than the second, while the opposite holds for the second variant. As a result, the mixing ratios between the test set and the synthetically summed inputs (used during training) differ significantll. For each variant, scSplit and the two top baselines (U-Net for LPIPS, denoiSplit for PSNR) were trained and evaluated on the unaltered real superimposed images. The results in Table show that scSplit consistently outperforms both baselines by substantial margin in PSNR across both variants, demonstrating robustness to variations in relative structure intensity.
Effectiveness on Downstream Segmentation Task. For the bleed throutthoough removal task (w E 0.7, 0.8, 0.9), we used the test set of the BioSR dataset to evaluate segmentation as a downstream task with Featureforest (max_depta) dept h= 9, numtrees=450. encoder=SAM2_11 _argge) a recently developed segmentation method 22 To avoid model bias, we manually annotated the ground truth and trained Featureforest using these annotations (as target) alongside model predictions (as input). If we had annotated the predictions instead, it would raise concerns about the consistency and quality of annotations when doing for scSplit's predictions as opposed to when doing the same for the baseline models. We trained 4 x 2 x 3 24 Featureforest models- one per model, channel, and mixing ratio. We show the results in Table 4 where the evaluation used the Dice dissimilarity from scipy (lower is better). Among all methods, segmentations from scSplit predictions best matched those the ground truth channel.
Model
Channel
Channel 2
W 0.7
0.8
w = 0.9
0.7
w 0).8
0.9
denoiSplit
0.077
0.073
0.065
0,064
0.061
0.056
SSpli 0.055
0,051
0.047
0,051
0.047
0.038
InDI 0.055
0.050
0.044
0,046
0.045
0.045
scSplit 0.048
0.039
0.035
0.038
0.032
0.026
Table 4: DICE dissimilarity scores for various models mixing ratios. scšplit achieves the best (lowest)
DICE dissimilarity across settings.

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Utility of SCIN. Its utility can be inferred by comparing InDI with our scSplito.s variant in Table I with scSplit, 5 outperforming by 1.2db PSNR on average across all regimes and all four datasets. Note that all hyperparameters for the InDI and Gen; networks of scSplito.5 are identical, and the only difference is in the normalization. Please find the ablation for the normalization module in Sup. Sec.[] One can also note its utility by comparing the performance of Reg network trained with or without our normalization scheme in Figure SarreJeeff left). We also present a comparison between SCIN and Instance Normalization in Sup. Sec. B as the latter can likewise address the issue we identified.
Utility of Aggregation and Reg network. Across Tables I and 2 scSpli outperforms the ablated network scSplit_oog agg on all tasks for the PSNR metric, thereby clearly justifying the utility of the aggregation operation. See Sup. Sec. for experiments with other aggregation methodologies. One can observe the utility of using Reg when comparing scsplit, with scSplit_ ogg-, with the latter variant outperforming the former across several tasks in Table It worth noung that the improvement is more pronounced with more asymmetric mixing ratios (Dominant and Weak regimes). We argue that scSplit.s 's assumption of w = 0.5 becomes reasonable in the Balanced input regime, leading to its competitive performance in this regime.
Degradation Analysis for Reg. In Figure [a), with the BioSR dataset, we analyze the performance degradation when using increasing incorrect estimates for w during inference. We evaluate scSplit using& fixed w (x-axis) in the inference, while the inputs have been created with a different w (legend). We find scSplit to be relatively stable to small differences between the assumed w and actual w. We support this claim qualitatively in Figure
Exploring Augmentations. One of the critical advantages scSplit and InDI have over other base- lines is that during training, they observe inputs with different mixing ratios, and so naturally, it makes it easier for them to outperform them. InDI, however, cannot leverage this advantage since it does not have the Reg network and is therefore forced to use = 0.5. In this experiment, we attempted to give this advantage the baselines through augmentations. We experimented with two different augmentations in the training procedure of puSplitp. the most powerful variant of j(Spit.. During training pSplitp, instead of creating the input inp by simply summing the two channel images, we instead compute inp = tCo + (1 t)cı, where is sampled from p(t). We work with two variants of p(t): (i) p(t)= = U0, 1] and (ii) p(t) as defined in Eq. 3 Results shown in Figure 4 demonstrate that these augmentations help ,Split, to improve performance for w further away from 0.5, along with some performance degradation for w = 0.5. However, scSplit still consistently outperforms the best of all three variants by 2.4db PSNR on average. We note that the suboptimal normalization settings for pSplit also contribute to this, which is analyzed in the Sup. Fig. S.3
5 Conclusion, Limitations, and Future Directions
In this work, we introduce scSplit, a network designed to simultancously address two key challenges in fluorescence microscopy: image unmixing and bleedthrough removal. Our architecture is explicitly designed to account for the severity of the superposition that needs to be unmixed. We also identify limitations in the normalization methodologies of existing image unmixing approaches and propose an alternative normalization strategy that is better suited for inputs with varying levels of superposition. Additionally, we developed an aggregation module that improves the estimation of mixing ratios.
Despite its strengths, scSplit has a couple of limitations that warrant future investigation. First, the current framework is not optimized for noisy data-though two-step approach (self-supervised denoising followed by unmixing) can be a suitable approach, an end-to-end solution could offer significant advantages. Second, extending scSplit to handle more than two channels would broaden its applicability. Finally, interference-batt assumption of input formation, and therefore the effectiveness of scSplit and other semantic unmixing methods 6 3 on such modalities remains to be evaluated.
imaging modalities may challenge the linear superposition
While scSplit is designed for fluorescence microscopy, its core principle of bringing severity cog- nizance into the inductive bias of the network could benefit general image restoration. In Sup. Sec. [ we do proof-of-concept experiment to show that our approach can enhance motion deblurring performance. However, adapting scSplit to natural images would require integrating task-specific inductive biases- exciting direction for future work.
10

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Acknowledgments
The authors thank Mauricio Delbracio and Peyman Milanfar from Google Research for useful discussions and technical guidance. This work was supported by the European Commission through the Horizon Europe program (IMAGINE project. grant agreement 21094250-IMAGINH core funding of Fondazione Human Technopole. We want thank the IT and HPC team at Human Technopole for access to their compute infrastructure and all members of the Jug Group and our image analysis facility NoBIAS for helpful discussions and support.
as well as
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: We introduce novel image unmixing network architecture scSplit capable of handling varying levels of superposition severity. The evidence of scăplit working across different superposition severity levels be inferred from its outperformance
multiple baseline methods in Table [ This outperformance also indicates that it indeed solves image unmixing and bleedthrough removal task. The benefit of regressor network assessed by comparing scSplit with InDI in Table In Section 3.2 we motivate the necessity
also be of the normalization module and provide the complete proof in the Sup. Sec. A.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results be expected to generalize other settings.
It is fine include aspirational goals as motivation as long is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification:
We discuss limitations and future work in Section 5.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model vell-specificattin, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested few datasets with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimess.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
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3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
Justification: In the Sup. Sec. A, provide the proof for our claim made in Section 3.2 (Equation?) 2)
Guidelines:
The answer NA means that the paper does not include theoretical results. All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged provide short proof sketch to provide intuition.
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4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: The training setup, along with all hyperparameters, mentioned in detail in the main paper and supplementary material. While the manuscript provides sufficient information for re-implementation, exact reproduction of qualitative and quantitative results may require access to our code, which is submitted along with the manuscript.
Guidelines:
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Supplementary Material for
scSplit: Bringing Severity Cognizance to Image Decomposition in Fluorescence Microscopy
Ashesh Ashesh, Florian Jug
Jug Group, Human Technopole, Milano, Italy
Inpul
Prediction
image Uhinking
Prodict
Variafons suparpostion
Figure S.1: Handling varying levels of superposition. For the objective of image unmixing task, superimposed images acquired with Fluorescence microscopy can have varying levels mixing the constituent structures. Additionally, insufficiently precise optical filtering often leads to 'bleedthrough' wherein structure of interest gets superimposed with a shadowed presence of another structure, scSplit uniquely addresses these varying levels of structural mixing in the superimposed input images. Unlike existing unmixing methods, scSplit's architecture adapts different degrees of superposition and accounts for the resulting variations pixel intensity distributions (inset plot in red), enabling effective input image normalization and leading to efficient unmixing across diverse mixing ratios.
A Severity Cognizant Input Normalization
In this section, we extend the formulations presented in Section 3.2 to accommodate images of arbitrary dimensions H W. Let peli,j] be a random variable denoting pixel intensity value present in c E C2 at the location (i,j). Let us now compute the mean (u(t)) and variance (o² of cr.
m(t)
Σ pll..ll
(1)
P i.j
and
d²()) Σ peli. uut)? 1.J
(2)
where is the total number of pixels in 6. Note that jut) and o (t) are also random variables. Their expected values E[u(()) and ([)(()) are typically used for normalization.
Next, describing v()) in terms of random variables po and pr. get,
m(t) = P
>>( ((1 t)pult, + tp (1
i
= (1 - 1) P
1
Σ
po pilii + p Σ [ili
1
(3)
1.j
(1 - ()) + (1).
Taking the expectation the above equation, we get
E'u(t)] (1 ()) (1))
(4)
S.1

---

Doing a similar analysis for the variance, we get,
1 Σ Bip.it, -
B[o²(t))
(5)
Next, we simplity Elpeli. and [[u(t)] to get
1 [1 = E - ro(t.]] (
+26 - jtpp
(6)
= -1 100
+26 - (1
E Bl((t))² = (1 - (0 +21 - ())
Using expressions derived above, the expression for [t) becomes,
Elo²(t)) (1 t)
E Ep B[{(O))²)
P
+1²
Σ
13 Epp -1 B[((1)
(8)
1 +2H(1 - t)(
Elpol 1pp [1 - E|x(O)E[|<()))
With biological data, the image acquisition process works in the following way: a random location on the specimen slide is picked and that is then captured to generate an image frame. So, all pixel locations can be assumed to be equally likely to capture any part of any structure. We therefore assume, Elpela, [j, R[pp (c, d] Va, b, c, d and Elp (a, b]] Ely [c, d]] Va, b, c, d. So, remove the pixel location and define Pt to be a random variable denoting a pixel in G,- We define E[pr] == Elpela, 6]] Va, 6 and [E[r]] Elp? (a, 6]] Va, b. The expression for [B(o²(t)) now simplifies to,
[[]²(0)= =1 (1 (1-
E B (l)()
1.J
+22
Eip - E[m(1)}
p
(9)
+21(1 1)(
E8 EPPoPI] - ([x(()][(((1)
P
1.J
(1 - 1) (E(p)) (0) +2 ( E(p())
+26(1 1) (E ((]())]]
(1 (1-t) (1-1)"=(((00) + + 2f t)oo P1),
where Cov(:::) is the covariance function. Now that we have the expressions for Elu(t)] and El)²(()), we consider a plausible normalization methodology where co and e₁ normalized using the following procedure: for every co in Co. we compute its mean and standard deviation. We average the mean and standard deviation values computed over all images from Co to obtain a global mean and global standard deviation. We use them to normalize every image. An identical procedure is followed for e1. In this case, by construction E [()(O)] Ejp(1)] 0 and [0) E[o²(1)) So, from Eq. El((()) 0. However, (t)) still remains the following function of t,
1.
1 [()) = (1 t) + 2 + 2f (all-t)Cooom t)Cov(po.Pz)
(10)
As discussed in the main manuscript. this causes serious issues during normalization.
S.2

---

B Instance Normalization: Another Way to Achieve Our Normalization Objectives
If one thinks about the normalization requirements we discovered in this work, one realizes that applying instance normalization (IN) in the first layer can, in principle, also mitigate the normalization issue we discovered for the semantic unmixing task. Instead of making expected mean to zero and expected standard deviation to one as in our approach, will ensure that for every input patch coming out from IN layer, its mean and standard deviation are zero and one respectively. It is simpler and therefore makes up for an attractive alternative approach. However, we found both empirical and domain-specific reasons led us to have the SCIN normalization approach we proposed in the main text.
For the empirical evaluation, we conducted experiments on the Hagen et al. dataset [29] using instance normalization. We trained two additional baselines: (1) InDI (firstIN), with instance normalization as the first layer, and (2) InDI (allIN), replacing all group normalization layers with instance normalization plus a first-layer instance normalization. Similar variants were also created for the scSplit network. Results presented in the Supplementary Table [S. show our original scSplit model outperforms most baselines. Among 'firstIN' and 'allIN' variants, the 'firstIN' variant performs better than the 'alIIN' variant. Results for the PaviaATN task with 'firstIN' are also reported in which case as well, scSplit has clear out-performance for the bleedthrough regime (Dom.) and is competitive in others. More specifically, scSplit outperforms scSplit (firstIN) across three input regimes and two datasets, with an average PSNR gain of 0.33 dB. Since both models share the same network architecture and incorporate correction of the normalization this performance gap as evidence of superiority of our normalization module over IN.
key innovations (a) the Reg network, (b) aggregation of t, and (c) performance gap could not be large and thus we consider
Dataset
Model
Dom.
Bal.
Weak. SSIM
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
LPIPS
Hagen al.
InDI (allIN)
36.5
0.987
0.026
32.4
0.968
0.060
27.9
0.914
0.132
Hagen al.
InDI (firstIN)
36.7
0,987
0.032
33.5
0.974
0.052
26.6
0.881
0.154
Hagen al.
scSplit (allIN)
36.6
0,988
0.025
32.4
0.967
0.061
27.9
0.916
0.131
Hagen al.
scSplit (fissIN)
40.1
0,993
0.016
34.0
0.976
0.051
29.0
0.924
0.129
Hagen al.
scSplit
40.9
0.994
0.011
33.9
0.977
0.046
29.3
0.934
0.123
PaviaATN
InDI (firstN)
28.8
0,950
0.102
27.1
0.903
0.150
21.3
0.768
0.248
PaviaATN
scSplit (firsIN)
33.5
0.975
0,042
27.7
0.906
0.172
24.8
0.825
0.440
PaviaATN
scōplit
35.1
0.977
0.033
27.6
0.907
0.555
24.3
0.823
0.377
Table S.1:
Comparing our normalization scheme (sc3plit) with using instance normalization (scSplit (first
Next we provide logical arguments which favor SCIN over IN for the task at hand. Instance norm has been reported degrade discriminative performance in tasks where intensity clues or instance specific contrast is relevant [33 [4]. In microscopy, intensity cues are important. For instance, the background can be casily distinguished from the 'content-less' interior of an organelle like nucleus simply by comparing average intensity value. However, instance norm can make it difficult as it normalizes per patch. This will be more true for smaller patch sizes, typically used for semantic unmixing (patch size of 64 and 128 were used by μSplit (3] and denoiSplit [2] respectively). A similar argument can be made for the Reg network. IN when applied to c distorts the structure of the distribution Cr, by eliminating statistical differences between individual images, whereas these remain preserved with SCIN. Applying IN to &, could actually negatively affect the ability of the Reg network to reliably estimate I, because by eliminating inter-image statistical differences, IN may discard the very signal that the Reg network requires to estimate t.
Finally, from the computational efficiency standpoint as well, our normalization approach SCIN is better. Our normalization module's extra computation occurs only once before training, when means and standard deviations for each t are calculated - fast rre-processin step (e.g., about 7 minutes for Hagen et al. in a naive implementation). After this, training (taking 3 days on Tesla V100 GPU) normalizes input patches using these precomputed values, adding no overhead during training. However, we provide evidence that the IN-based approach could actually be more computationally demanding, particularly when using smaller patch sizes. IN internally needs to compute the standard deviation over the full frame for each input patch, and this computation is performed within the datasct class, and therefore must happen on the CPU. With frame dimensions of several thousand
S.3

---

pixels found typically in microscopy datasets (e.g.. 2720 x 2700 for PaviaATN, 2048 x 2048 for Hagen et al., 4096 x 4096 for Chicago-Sch23 [ ). we conducted quick estimation: On our high- performance cluster (Intel(R) Xeon(R) Gold 5220 CPU @ 2. 2.20GHz), it takes around 28 milliseconds (measured with %timeit in ipython) to run torch.nn.Inseeeee..... InstanceNorm22(() on a 3000 3000 image. For training schedule of 450K iterations with batch size 8 (our configuration), this would amount to about 28 x 10-3 3 x 450K X 8/3600, which is around 28 hours of added training time solely due to the IN operation. Even with 4 workers (our configuration), this step alone would still require 7 hours. This is about 10 percent increment in training time for our task. Additionally, when using smaller patch sizes, either batch size or iteration count needs to increase if we want the training to the data 'same number of times', which would only increase the computational cost. For instance, just halving the patch size 256 would increase the extra computation cost to 28 hours.
C
Ablation of Normalization Module
Model
Dom.
Bal.
Weak.
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PaviaATN
35.1
0.978
0.032
25.9
0.895
0.202
23.7
0.813
0.492
Hagen
39.4
0.990
0.017
30.8
0.962
0.067
27.8
0.923
0.120
HTT24
42.7
0.992
0.003
37.1
0.973
0.011
33.7
0.934
0.034
BioSR
39.3
0.979
0.017
33.6
0.936
0.059
28.1
0.874
0.146
Table S.2: Model performance (PSNR, SSIM, LPIPS) without SCIN module.
Here, we conduct an ablation study where the scSplit model was trained without SCIN module. Instead, we used the commonly adopted approach in iterative inference models, where the two images are normalized first using mean-std normalization and then combined via convex combination to form the intermediate input Tz. In the supplementary table S..2 we present the results of scSplit using this 2-image normalization scheme across four datasets. For each task, we trained the Reg and networks under this normalization approach. Across all tasks and all input regimes, it evident that the PSNR values of the original scSplit model (as reported in Table I of the main tex() outperform those reported here, with the sole exception of the task on PaviaATN dataset under the dominant input regime, where the PSNR values equal.
It important to highlight a limitation in the normalization approach used by current semantic unmixing methods 3 2 6 These methods typically estimate a single set of mean and standard deviation values from all input data and apply this global normalization to input patches from the training, validation, and test sets. In practice, this presents challenge: test images acquired from microscopes often exhibit distinct intensity distributions compared to the training data. Therefore, would be more appropriate to normalize test images using statistics computed specifically from each newly acquired dataset. Some existing methods K performed well using global normalization because their train, validation, and test images originated from the same acquisition session. In Sup. coatistissshhrre
Tab.[S.8) we report the performance of μSplit variants when global normalization across train, validation, and test-are are used. Notably, scSplit (shown in Table 1) still achieves superior results. Nevertheless, we emphasize that applying global normalization in this manner is not practically feasible for real-world inference scenarios.
D Thoughts on Iterative Inference
Our implementation of InDI has the possibility of doing iterative inference with any number of steps. With minimal change one can also perform iterative inference with out scSplit. However, in this work, we have consciously avoided iterative inference and have always performed I-step inference. In the next few paragraphs, we explain the rationale behind it.
In Figure of InDI 4 the authors quantitatively show that more iterations lead to worse PSNR (higher distortion) but improved perceptual quality. The same is shown for three datasets in Figure 9 of InDI, that shows a monotonous drop in PSNR when increasing the number of iterations, with total drop being atleast 2db PSNR in all three cases. When working with predictive models on biological data, one can argue that in the perception-distortion tradeoff (35] the motivation is to get the model with better fidelity to the recorded image (lower distortion). This would not be true if the motivation
S.4

---

was to generate synthetic datasets, in which case better perceptual quality might be the major goal. With focus on better fidelity, we use one step prediction for both InDI and inDiSplit. Note that training in InDI is not iterative and so this choice does not affect in any way how InDI is trained.
That all being said, iterative inference in indiSplit can done in the following way: Instead of starting from & = 1 as done in InDI, one needs to start from the value of estimated with Reg network. A, This implemented in to ensure that [z) ht/d//dmmmmmaaeeeeeeeeeeeee www.lesdeeeeee.... //ndii. py). The one change that needs to happen and E (x))) 1, where p() and o(( represents the mean and the standard deviation operators. This can easily be achieved by a normalization step in each step of the iterative inference.
the unit decrement in can simply be computed A Setart/totalSSie
code (see line 93 in model/ddpm
E Quantitative Evaluation Methodology
In this section, we illustrate the methodology used to compute the results presented in Table I of the main manuscript by taking the following example. Let us describe the performance evaluation process for a specific value of w. such as w = 0.7. To assess model's performance for w = 0.7 on a given dataset, we first generate imputs with 0.3 using Equation and evaluate the performance metrics for Co (using Geng). Next, we generate inputs with / = 0.7 and evaluate the performance for G1. The average of these two metric values represents the model's overall performance for w = 0.7. Each metric is computed on individual image frames, and the average performance reflects the mean metric value across all test set frames. The corresponding standard errors (computed over all test frames) for Table 1, averaged across both channels, are provided in Table S.10 For Table 2, the standard error values, averaged across both channels, are presented Table S.9
F Normalization Details for Our Baselines
The official implementations of various μSplit variants and denoiSplit are publicly available, and they share an identical input normalization scheme. During training, all pixels from images both sub-datasets Co and Ci are aggregated into a one-dimensional array, and the mean and standard deviation of this array are used to normalize all input images the validation and test sets. is important to note that the set of normalized patches from training data does not have zero mean and unit standard deviation. So, similar to InDI, the optimal normalization scheme which should be employed on test images is easy to obtain.
For evaluating these baselines on the tasks presented in Table we adhere to their normalization scheme with one modification: for each mixing ratio f, the mean and standard deviation are computed using pixels exclusively from the input images ca. Note that when evaluating test images, we cannot assume access to individual channels and so cannot use their normalization scheme. Note that this scheme is applied solely to these baselines during evaluation.
G Hyper-parameters and Training Details
We use a patch size of 512 to train scSplit, InDI, U-Net and denoiSplit networks. For μSplit variants, we kept the patch size as 64, which is used in their official implementation. The reason is that, spite of using 64 as the patch size, they effectively see the content of 1024 x 1024 sized region surrounding the primary input patch. This because the presence the LC module they have their network which takes as input additional low-resolution patches centered on the primary patch but spanning larger and larger spatial regions. For training Gen; networks, we use MAE loss and for training Reg network, fair comparison between InDI and scSplit, we used the same parameter count, non-linearity, number of layers etc. between them. We used MMSE-count of 10 to compute all metrics. In other words, for every input, we predicted 10 times, and used the average prediction for metric computation. All metric computation has been done on predictions of entire frames (and not patches).
use MSE loss. We use Adam optimizer with a learning rate of 1e 3. To have
For Hagen et al. dataset, to allow methods to compare with pretrained models of ySplit variants, we followed ySplit code of applying upper-clip to the data at 0.995 quantile. We upper-clipped the data at intensity value of 1993. This corresponds 0.995 quantile of the entire training data. Similarly, for PaviaATN, the upper-clipping operation was done at 1308 value.
S.5

---

GT
Mean
Median
Mode
WgtSum
WgtProd
0.00
0.13
0.12
0.11
0.14
0.15
0.10
0.15
0.14
0.10
0.16
0.16
0.20
0.21
0.20
0.13
0.20
0.20
0.30
0.31
0.28
0.27
0.29
0.27
0.40
0.43
0.41
0.35
0.42
0.40
0.50
0.54
0.53
0.66
0.54
0.51
0.60
0.64
0.64
0.61
0.63
0.61
0.70
0.72
0.72
0.74
0.71
0.69
0.80
0.77
0.78
0.79
0.77
0.76
0,90
0.80
0.79
0.78
0.79
0.80
1.00
0.80
0.80
0.78
0.80
0.81
Table S.3: Quantitative evaluation of different aggregation methodologies on BioSR data. First column is the ground truth and all other columns the aggregated predictions using different aggregation methodologies.
GT
Mean
Median
Mode
WgtSum
WgtProd
0.00
0.13
0.10
0.09
0.11
0.11
0.10
0.14
0.12
0.10
0.12
0.12
0.20
0.25
0.23
0.22
0.22
0.24
0.30
0.35
0.35
0.35
0.34
0.36
0.40
0.45
0.45
0.46
0,45
0.46
0.50
0.53
0.54
0.54
0.53
0.55
0.60
0.61
0.62
0.64
0.61
0.63
0.70
0.69
0.70
0.71
0.69
0.71
0,80
0.78
0.80
0.79
0.78
0,80
0.90
0.87
0.89
0.87
0.86
0.87
1.00
0.92
0.96
0.96
0.93
0.92
Table S.4: Quantitative evaluation different aggregation methodologies HTT24 data. First column is the ground truth and all other columns the aggregated predictions using different aggregation methodologies.
H Different Aggregation Methodologies
In this section, we experiment with different ways to aggregate the estimates of the mixing ratio I. We iterate over the test set and for each patch, get estimate of l. We tried several ways to aggregate the estimates. We aggregated the estimates using mean, median and mode as three different ways. Next, based the hypothesis that mixing ratio estimates predicted from patches containing both structures could be more accurate than those from patches dominated by a single structure, implemented two additional aggregation methods. For them, replicate the scalar mixing ratio predictions to match the shape the input patches. We then tile these replicated mixing ratio predictions that they have the same shape the full input frames. Using t 0.5, first make a rough estimate of both channels, & and èj- We then take the weighted average of the pixels present in the tiled mixing ratio frame, with weights computed by normalizing (I) + ? and (II) &n éj. So, pixels in which both structures are present will get a higher weight. We call them WgtSum (corresponding
and WgiProd (corresponding II). We do not observe any significant advantage for any of the above mentioned aggregation methods in Tables S.3 S and S.5 and so we resort to using mean as our aggregation method all tasks.
I On Design of Gen;
As described in the main text, we worked with setup which requires one generator network per channel. While one can envisage an alternative implementation using single generative network with two channels instead of two separate networks Geno and Gen,, extending it to multiple channels with each channel contributing differently to the input, which is our future goal, would become complicated and so we decided on this cleaner design.
S.6

---

GT
Mean
Median
Mode
WgtSum
WgtProd
0.00
0.13
0.11
0.09
0.13
0.13
0.10
0.18
0.16
0.14
0.18
0.18
0.20
0.24
0.22
0.17
0.24
0.24
0.30
0.34
0.33
0.26
0.32
0.32
0.40
0.43
0.42
0.44
0.40
0.40
0.50
0.52
0.51
0.52
0.49
0,48
0.60
0.60
0.58
0.57
0.56
0,56
0.70
0.69
0.68
0.61
0.66
0.65
0.80
0.78
0.78
0.76
0.76
0.75
0,90
0.87
0.88
0.88
0.88
0.87
1.00
0.89
0.90
0,90
0.91
0.90
Table S.5: Quantitative evaluation of different aggregation methodologies on HTLIF22 data. First column is the ground truth and all other columns the aggregated predictions using different aggregation methodologies.
Lassumed
PSNR
0.3
35.0
0.5
37.3
0.7
36.2
1.0
32.4
Table S.6: Evaluating performance of scăplit on synthetic inputs created from the test sub-dataset of GoPro motion deblurring dataset. Informally speaking. half of the haze was removed from the original test images using Equation [1 scSplit indeed was able to yield superior performance when was 0.5 during inference.
J Application to Natural Images
For image restoration tasks, is evident that reality, images with different levels of degradation exist and therefore, method that is cognizant of the severity of degradation is expected to have advantages.
However, to make our idea applicable to image restoration tasks on natural images, one would need account for the differences between the image unmixing task performed on microscopy data and those tasks. For example, in fluorescence microscopy, we made plausible assumption that single acquisition amounts to single mixing ratio. However, in motion deblurring task, portion of the image containing moving object, e.g. static object, like a wall. So, one would need to account for this spatial variation of the degradation. For de-hazing and de-raining tasks, similar challenge holds. Objects more distant from the camera typically have more degradation. So, to handle such spatially varying degradations a diligent manner, t, the input to scSplit also needs to be spatially varying and therefore should not remain a scalar. Secondly, for the image unmixing task described this work, we have access to the two channels, and we correctly define the mixing ratio. However, with these image restoration tasks, one does not have access to the other channel, which would be pure degradation. One instead has access to the clean content and intermediately degraded image. So, = 1 will have different connotations for the image-unmixine task described in this work and image restoration tasks on natural images, which need to be properly accounted for.
will have more severe blurring when compared to
However, as a proof concept, we trained scSplit with just one generator network Geno for the motion deblurring task GoPro motion deblurring dataset [36). Since all the variations of severity of degradation present in the training data were explicitly mapped to t = during training all degraded images belong to C1, which means = 1 for all such images and this is irrespective of their qualitative degradation levels), it is expected that during inference, = 1 will be the optimum choice on the test sub-datased provided in this dataset.
So, enhance the diversity of the degradation, we took test set of the GoPro dataset and created a set of less degraded input images, by simply averaging the inputs with the respective targets i.e.
0.5x 0.5y',
(11)
new
S.7

---

Actual Input
Synthesized Input
Pred (t-0.5)
(t-1.0)
Ground Truth
Figure S.2: Here, we qualitatively show the potential benefit of regulating the restoration process by making the network cognizant severity of degradation present in the input image. Predictions are made on 'Synthesized Input', which created doing the pixelwise average of Actual Input and the ground truth image. This essentially yields less blurry image. In reference frame of the trained scSplit, = 0.5 would the optimal inference setting for these synthesized inputs. We cherry picked few 100 x 100 size crops where the difference between the prediction made by scSplit with 0.5 and with = 1.0 was clearly visible. We also show quantitative evaluation all similarly synthesized input frames from the test sub-dataset in Table S.6
S.8

---

where x' is the original input image and y² is the corresponding target image. Next, we evaluate the scăplit network on all veew images while using different values of during inference. We show the results in fable|S.6)ande the qualitative results in Figure S.2
In this case, one indeed observes that 0.5 is the optimal choice. Interestingly, even slightly off estimates of & (t 0.3, and & = 0.7) also yield superior performance over t = 1.0. This proof-of- concept experiment shows that when handling blurry images with lower levels of degradation, is not an optimal choice. But due to the non-trivial differences between our current image unmixing task and these restoration tasks, as outlined above, we plan to take up the task of adapting scSplit for natural images in a separate work.
K Analyzing the Effect of Precision
In the official configuration of SSSlit variants, we found that the training was done with bit floating point precision. The pre-trained models for μSplit are also trained with 16 bit precision. However, other baselines and scSplit are trained with 32 bit precision. So, we trained ySplitt with 32 bit precision to assess the performance difference. We compare the performance in Table [S.7 Across the three input regimes, one observes the average PSNR increment of 0.3db, MS-SSIM increment of 0.002 and LPIPS decrement of 0.004 when one uses 32 bit floating point precision. By observing Table 1, is evident that this change smaller than the advantage scSplit has across all three input regimes.
L Selecting Number of Intervals
During training, we chose the number of intervals n used to partition the domain of mixing ratio, which is [0, 1], based on the principle that the interval width should not exceed the error in estimating t using Reg. If it did, we would accept reducing the mixing ratio granularity that the Reg network is, in principle, capable of giving us. For example, the HTLIF24 derived task, the mean absolute error (MAE) between the predicted and actual t values within the valid range [0.1, 0.9] is 0.03 (see Supple- mentary Table S3, column 2). Therefore, any interval size smaller than 0.03 would be appropriate for this task. Following this reasoning, we selected smaller interval size of 1.01-insultig in 100 intervals to ensure the interval width remained sufficiently low across all tasks.
Since interval count is a paper-parameter rather than a learnable parameter, and we do not perform explicit optimization on would be inaccurate assert that 100 is the best choice universally. Our selection of 100 was based on an intuitive argument presented in the previous paragraph. However, there is no downside to choosing sufficiently large number of intervals (apart from the one time compute required to estimate the mean and std for each t), so one may opt to do so.
M Qualitative Performance Evaluation
For different values of w, we show the qualitative results for the Hagen et al. dataset in Figures 5.4 S.5 and S..6 For the BioSR dataset, results are shown in Figures S.7 S.8 and S.9 For the HTT24 dataset,
results are shown in Figures S. S. and S.12 For the HTLIF24 dataset, results are shown in
Figures S.13 S.14 and $.15 For the PaviaATN dataset, results are shown in Figures S.16 S.17
and
Dominant SSTM
Balanced SSIM
Weak SSIM
PSNR
LPIPS
PSNR
L.IPS
PSNR
L.IPS
SSplitt y (16-bit)
37.8
0.918 0.918
0.066
33.5
0.959
0.051
25.7
0.738 0.741
0.291 0.284
SSpliit, (32-bit)
38.1
0.065
33.9
0.962
0.045
25.9
Table S.7: Analysing the effect of training with 32 bit training with 16 bit floating point precision. In pSplit variants, the official configuration is to train with 16 hit floating point precision.
S.9

---

UIO.
40
40.0
desp-LC UjO.
03.0
35
37.5
scipit
31.5
35.0
35.0
-3
32.5
25
30.0
27.5
25.0
25.0
0.2
deepelC C
dcep-LC Tha
45-
docp- CC U10. 1) TrainN
dcop LC UjO. 1]
45-
0cop LC Bo.661 Train
deep-1
40
ScSplt:
sc5pit
40
sc5pltt
33
30
30
0.2 0.4
0.6
0.8
0.2 0.4
0.6
0.8
0.2
0.4 0.0
W 0.8
Figure S.3: This figure investigates the influence of normalization the performance of pSplit empha- sizing its inferior outcomes relative scSplit. Notably, other JuSplit variants and denoiSplit share the normalization setup as jsSplit making this analysis broadly applicable to several existing unmixing methods. We evaluate ySplit and two of its variants, each utilizing distinct augmentation strategies, as outlined in the main manuscript's 's Fig 4. Performance is assessed under two normalization schemes: (I) the default approach, where and standard deviation statistics are calculated separately inputs with a specific u. The results demonstrate that all SSplit variants underperform compared to scSplit under both normalization strategics. Furthermore, we note that μSplit trained with uniform normalization statistics, performs more effectively under the default evaluation sctup, which discussed in the main manuscript is reasonable choice given the intensity variations across different microscopy acquisitions.
derived from the training data, and (2) w-dependent method, where
Dataset
Dominant
Balanced SSIM
Weak SSIM
PSNR
SSIM
LPIPS
PSNR
LPIPS
PSNR
LPIPS
Inp vs Tar
34.1
0.973
0.047
25.1
0.889
0.148
21.2
0.784
0.243
U-Net
33.5
0.976
0.038
33.4
0.960
0.066
23.3
0.840
0.190
Hagen et.
Splitt
34.2
0.974
0.044
32.3
0,959
0.071
23.8
0.843
0.187
pSplit n
34.6
0.971
0.041
32.4
0.957
0.068
24.5
0.842
0.189
sSplit, p
33.9
0.975
0.039
33.6
0.963
0.061
24.1
0.849
0.179
Table S.8: This table, analogous Table dataset across the same three input categories. Here, we utilize the mean and standard deviation computed from the training data for normalization. Since SSplit variants are trained with these statistics, they achieve superior performance with this normalization setting, since the test images share the same intensity distribution the training data due being from the same acquisition. However, as outlined the main manuscript, this approach not viable for evaluating images from different acquisitions, where intensity distributions may vary. Notably, scuplit surpasses even these results, demonstrating its robustness and superior performance.
main manuscript, evaluates performance on Hagen
HT-LIF24
HT-T24
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
U-Net
.692
.002
.002
.613
.006
.022
sSplit,
.635
.001
.002
.614
.007
.002
SSplit z
.697
.002
.002
.624
.007
.002
SSplit
.734
.002
.002
.626
.008
.002
denoiSplit
.675
.001
.002
.574
.005
.003
InDI
.560
.002
.002
.596
.007
.004
scSplit,.s
.704
.001
.001
.627
.007
.002
scSplit agg
.669
.002
.001
.657
.008
.002
scSpht
.736
.001
.001
.627
.007
.002
Table S.9: Standard error estimates in Table (channe--verraged).
S.10

---

Sppli
InDi
Target
PSRK SLM
PAR 29
PANK 201
PSRA 2010
PAN 20.1
PSNR: 12.0
20
PSN
Input
pSplit yg
denoiSpiut
scSplit
Tirget
PABA:
PANAL
PSKC: 15.5
PSNA:
PSHN 27.
PSNA
Input (w 0.71
ppplic
denuiSplix
InDi
ScSplit
Target
PAKA
FORR
PANR
Figure S.4: Qualitative evaluation Hagen al. each panel, we show the input frame (top-left) and the zaomed-in input patch (bottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row, We also report PSNR values for the patch shown. The w value reported on top of the input column for the first channel. naturally becomes w for the second channel.
S.11

---

Sppli
denoiSielii
InDi
Target
PSRV
PANA J0H
PANK
PARK
PSRT 20.3
PONT: 20.2
2500:220
PONTC: 30.0
Input
pSplit
denoiSplut
scSplit
Tugget
PANA:
PANA
PShe::25 30
PSAP
FSM
PONA
Input (w 0.41
SSpli
denniSplit
InDi
ScSpiit
Tareet
PAKR
PORR
PANR
Figure S.5: Qualitative evaluation Hagen al. each panel, we show the input frame (top-left) and the zaomed-in input patch (bottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row, We also report PSNR values for the patch shown. The w value reported on top of the input column for the first channel. naturally becomes w for the second channel.
S.12

---

Input
Sppli P
denoiSietii
InD
PSRK
PAN 20
PSNN
PSRN
PANK: 32.9
PSNT: 35.3
PSMB: 39.0
PSNI: 20.4
Ingut
pSplity
denoiSpur
scSplit
Tugeet
PANA:
PAR
PSKR:
15AA: 21
PSHN:
PSNA: 20.0
Input (w 0.11
pSpli
denniSplit
InDi
ScSplit
Tuget
PakA 2411
PANR
Figure S.6: Qualitative evaluation Hagen each panel, we show the input frame (top-left) and the zaomed-in input patch (bottom-leftt) for which we show the predictions and the targets (last col) for the two channels, one in each row, We also report PSNR values for the patch shown. The w value reported on top of the input column for the first channel. naturally becomes w for the second channel.
S.13

---

SSpli
denoiSpeii
InDi
PSNEL 54.2
PSNE: 35.5
PSWR 31.5
PSNR 36.7
PSNR
17.
PONR 17.
PONR 16.0
Input
pSplit yo
denoiSplur
scSplix
Tirget
PSNRU $5.4
PSMEU 35.0
PSURU $2.5
PSAR
POND: 200
PONR 36.7
POUR 20.7
POUR 23.5
Input (wr 0.71
p:Split
denmiSplit
InDi
ScSplit
Target
PSNRI
PSNE:
PSME
POULL 27
PONR 26-2
Figure Qualitative evaluation BioSR dataset. In each panel, we show the input frame (top-left) and the zaomed-in input patch (bottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row, We also report PSNR values for the patch shown. The w value reported on top of the input column for the first channel. naturally becomes w for the second channel.
S.14

---

5Syli 22
denoiSiliit
InDI
PSNR: 33.6
PSNE 36.5
PSIR 32.5
PSARI 33.5
PANR
PSDR 26-2
PSNR 12.5
Inpur
pSplit yg
denoiSplit
scSplit
Tirget
PSNKU
PSNEL 20.6
PSSEL 32.1
PSNR 32
PSUDL 20.5
PSUDL 25.5
POOL 20
POUR 35.
Input tsr 0.41
SSSpitt
denmiSplit
InDi
ScSplit
Target
PSNR:
PENAL 23.
PANL
PONDL 23.
PONR 200
Figure Qualitative evaluation BioSR dataset. In each panel, we show the input frame (top-left) and the zaomed-in input patch (bottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row, We also report PSNR values for the patch shown. The w value reported on top of the input column for the first channel. naturally becomes w for the second channel.
S.15

---

5Spli
denoiSistit
InD
PSHEL 20.0
PSNEL 2010
POWR 31.5
PSNR: 32.1
PSNR 35.8
PSR
PSNR 35.5
Inpur
pSplit pg
denoiSplur
scSplit
Tirget
PSNU:
PSMI: 22.2
PSNR 23.2
PSAR 2477
PSNDU20 25.3
PONDL 20
POUL 32
POURL 162
Input (w
0.11
pSplit
SenmiSpli
1nD1
Splpi
Target
PSNR:
34.5
PONE
Figure Qualitative evaluation BioSR dataset. In each panel, we show the input frame (top-left) and the zaomed-in input patch (bottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row, We also report PSNR values for the patch shown. The w value reported on top of the input column for the first channel. naturally becomes w for the second channel.
S.16

---

SSpli
denoiSiliir
InDI
Paeel: 29
PINE- 403
PSME 42-4
PSNR 33.5
PSNR
203
PSR 26-7
PSRR 23
Input
pSplit yo
denoiSplut
scSplit
Tirget
PSNI:: S0.8
PMN 36.7
PSNB 41.
PSNR 47.3
PONU: 20.5
PSNR: 20-7
POUR 20.6
POIR 25.0
Input (w 0.7]
pSplit
denniSplix
InDi
SeSplit
Tagee
PSNK:
PSNE:
PSNR:
PSM:: 20.0
PSNR 23.5
Figure S.10: Qualitative evaluation for HTT22 dataset. each panel, we show full input frame (top-left) and the zoomed-in input patch (hottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown. The value reported top of the input column is for the first channel. It naturally becomes 1 for the second channel.
S.17

---

SSpli
denoiSiliir
InD!
PSNEL: 40.3
PSNEL 40.9
PSWR 43.2
PSNR 42.3
PAN
26.8
PSDN 29-3
PSNR 29.0
Input
pSplit yo
denoiSplu
scSplit
Tirget
PSNEU
PSMR 42.8
PSMR 43.8
PSH 43.
PSNB: 32.5
PSNR: 33.5
PDR 32.0
POUR 32-7
Input (w 0.41
SSplit
denniSplit
InDi
S-ppi
Taret
PSNK
PSR
PSW
PSR 20.3
2SMR: 32.8
POHR: 33.
Figure S.11: Qualitative evaluation for HTT24 dataset. each panel, we show full input frame (top-left) and the zoomed-in input patch (hottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown. The value reported top of the input column is for the first channel. It naturally becomes 1 for the second channel.
S.18

---

SSpli
denoiSielia
InD
PSNEL: 34.3
PSNE: 36-7
PSIR 32.5
PSNR 35.4
PSNR
PSRR 33.7
PSRR 43.0
Inpur
pSpli g
denoiSplr
scSplit
Tirget
PSNUU 32.0
PSMR: 32
PSMR 29-3
PSN 35.9
PSND: 24.5
PSNR: 32.4
POUR 33,0
POUR: 38.9
Input (s 0.11
SSplit
denmiSplix
InDi
Sclpiit
Taree
PSNR
PSN
PSN
PSM:: 26-7
PSNR 42-4
Figure S.12: Qualitative evaluation for HTT24 dataset. each panel, we show full input frame (top-left) and the zoomed-in input patch (hottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown. The value reported top of the input column is for the first channel. It naturally becomes 1 for the second channel.
S.19

---

5Spli g2
denoiSiliiz
InDi
PSNBL 25.8
PSNE- 35.0
PSWR 31.5
PSNR 46.4
PSNR
31.3
PSDR 32.3
PSRR 36.5
Input
pSplit po
SenoiSplut
scSplit
Tirget
PSNK:
PSNI: 20.3
Potet $2.9
PSNR 42.5
PSNB: 25.3
PSNR: 32.6
POUR 34.3
POUR 36.7
Input (w 0.71
pSSpitt
denuiSplii
InDi
ScSplit
Target
PSWB:
PSNB:
PSNB:
PSN: 35.7
PSNR 37.0
Figure S.13: Qualitative evaluation for HTL.IF24 dataset. each panel, we show the input frame (top-left) and the zoomed-in input patch (hottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown. The value reported on top of the input column is for the first channel. It naturally becomes 1 for the second channel.
S.20

---

denoiSielir
InDi
PSHEL 20.2
PSNE: 30.2
PSWR 34.3
PSNR 45.
PSNR
PSD 41.5
PSRR 41.9
Inpur
pSplit po
denoiSplur
scSplix
Tirget
PSNBU 38.0
PSMBL 38.0
PSARL 37
PSNR 3P.0
PSMB: 43.5
PSNR: 40
PDU 46
POUR 45.9
Input (w 0.41
pSplit
denmiSplit
InDi
ScSpiit
Taree
PSNA::
PSN4: 42.0
PSNR: 40-3
PSNR: 40.3
Figure S.14: Qualitative evaluation for HTLIFF24 dataset. each panel, we show the input frame (top-left) and the zoomed-in input patch (hottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown. The value reported top of the input column is for the first channel. It naturally becomes 1 for the second channel.
S.21

---

SSpli
denoiSieliz
InD!
PSNE:: 26.2
PSNE: 30.0
PSWR 35.7
PSNR 36.5
PSNR
PSDN 40-8
PSRR
Inpur
pSplit po
denoiSplu
scSplix
Target
PSNKU
PSMR:
PSMR 34.4
PSNR 37.2
PSNAU 43.3
PSNR: 40.4
PDU 46.9
POUR 48.9
Input (wr
0.11
pSplit
denmiSplix
InDi
scSplit
Target
PSNR
PSNE:
PSNR: 20.4
PSMR: 42.3
PSNR 42-4
Figure S.15: Qualitative evaluation for HTL.IF24 dataset. each panel, we show the input frame (top-left) and the zoomed-in input patch (hottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown. The value reported on top of the input column is for the first channel. It naturally becomes 1 for the second channel.
S.22

---

SSpli n
denoiSieiiz
InD!
PSMEL 32.8
PSNB: 29.4
PSWR 30.7
PSNR 42.1
PSNR 14.3
14.6
PSR 14.1
PSAR 23.4
Input
pSplit go
denoiSplii
scSplix
Target
PSNU: 25.5
PSMI: 25.6
PSMR: 28
PSNR 40.2
PONB: 25.7
PDNR: 16.3
PDR 35.0
POUR-2222
Input Es 0.71
SSplit
denniSplit
InDi
ScSplit
Target
PSNR:
PSWR
PSN
PSMB:
PSNB: 29.2
PSNR: 24.2
Figure S.16: Qualitative evaluation PaviaATN dataset. each panel, we show the full input frame (top-left) and the zoomed-in input patch (hottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown. The value reported on top of the input column is for the first channel. It naturally becomes 1 for the second channel.
S.23

---

denoiSplii
InDi
PSMA: 22.9
PSNE: 23.9
PSHR 22.4
PSNR 31.0
PSMR
25.3
PSDR 19.3
PSRR 23.5
Input
pSplit gg
denoiSppii
scSplit
Tirget
PSNKU
PSMT: 24.8
PSNR: 23-5
PSAR 26-1
PDNB: 20.2
PSNR 25.5
PDR 29.5
POUR: 25.2
Input (w 0.41
pSplit
denniSplit
InDi
ScSplit
Taree
PSWR:
PSAR
PSHB:
PSMR: 20.3
PSN:: 22-4
PSNR: 21.5
Figure S.17: Qualitative evaluation PaviaATN dataset. each panel, we show the full input frame (top-left) and the zoomed-in input patch (hottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown. The value reported on top of the input column is for the first channel. It naturally becomes 1 for the second channel.
S.24

---

pSpli
Tirget
PSME: 23.0
PANR: 23.5
POR 27.8
POUR 28.5
PSMB: 27.6
PSNB: 22-8
PSDB: 29-3
PSHR: 28.7
Inpurt 0.2)
p-ppli
denoiSpelt
SeSplir
Tirget
PSNR:
PSMR: 10:4
PSUR: 26-8
PSNR 27.2
PSMR: 25.2
PSNR 15.9
PSUR 30.4
PSAR 35.7
Input (s
0.11
مSplitz
denoiSpliz
InDi
ScSplit
Tureet
PSNR:
PAMA:
POUR 20-9
POWR:
Figure S.18: Qualitative evaluation for PaviaAT'N dataset. In cach panel, we show the input frame (top-lcft) and the zoomed-in input patch (bottom-left) for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown. The value reported on of for the second channel.
the input column is for the first channel. naturally becomes
1n01
1.30
IDlistd
InDistd
0.80
scSpit-5dd
scSpilt-std
scSplt-.td
1.25
0.90
0.78
0.75
1.35
0.74
0.80
1.05
1.00
0.70
0.70
0.68
0.90
0.0
0.2
0.4 0.6
0.0
0.0
0.2
0.4
0.5
0.8
0.0
0.6 0.8
mixing factors using 2000 randomly sampled 512x512 image pairs (co, e1): ): (a) Supervised image restoration models like InDI [4] normalizes co and eı separately before interpolation, resulting in input patches with standard deviation strongly correlated with w: (b) our proposed method decouples this relationship. Results across Hagen et al. (left), HTLIF24 (center), and BioSR (right) datascts demonstrate reduced dependency with approach.
Figure S.19: Analysis of input patch variability
S.25

---

Dataset
Dominant
Balanced
Weak
SSIM
LPIPS
TPIPS
U-Net
0.3
0.003
0.003
0.5
0.007
0.007
0.6
0.015
0.014
aSplitz
0.015
μSplit,
0.8
0.004
0.004
0.6
0.005
0.006
0.6
0.015
0.015
pSplitt
0.7
0.003
0.004
0.6
0.004
0.005
0.6
0.015
0.013
Hagen
denoiSplit
0.005
0.012
0.005
0.013
0.020
al
MicroSplit
0.7
0.004
0.012
0.7
0,004
0.012
0.6
0.015
0.019
InDI
0,003
0.004
0.7
0.004
0.005
0.013
0.012
scSplitg.s
0.002
0.003
0.6
0.003
0.004
0.6
0.013
0.012
scSphi coo
0.5
0.001
0.001
0.5
0.003
0.004
0.5
0.007
0.010
scSplit
0.5
0.001
0.001
0.5
0.002
0.004
0.6
0.007
0,010
U-Net
0.7
0.001
0,002
0.7
0.001
0,001
0.8
0,0055
0,004
aSplitz
0.7
0.002
0.002
0.7
(L001
0.001
0.8
0.005
0.004
#Split,
0.002
0.002
0.8
0.001
0.005
0.004
0.7
0.002
0.002
0.7
0.001
0.001
0.8
0.005
0.004
denoiSplit
0,002
0.002
0.6
0.001
0.002
0.005
0.005
HTLIF24
MicroSplit
0.002
0.002
0.6
0.002
0.005
0.005
In]
0.7
0.002
0.001
0.7
0.001
0.001
0.7
0.003
0.004
0,001
0.001
0.8
0.001
0.001
0.005
0.004
scSplit
0.8
0.000
0.000
0.7
0.001
0.001
0.8
0.003
0.003
scSplit
0.8
0,000
0.000
0.7
0.001
0.001
0.7
0.003
0.003
U-Net
0.003
0.005
0.4
0.004
0.006
0.014
0.015
Splitt
0.4
0.004
0.005
0.2
0.004
0.006
0.6
0.011
0.014
uSplit
0.4
0.004
0.004
0.2
0.004
0.006
0.7
0.013
0.016
pSSpiit,
0.004
0.007
0.3
0.005
0.007
0.5
0.011
0.014
BioSR
denoiSplit
0.5
0.003
0.008
0.2
0.004
0.010
0.7
0.012
0.019
MicroSplit
0.003
0.007
0.3
0.003
0.010
0.7
0.013
0.019
InD1
1.0
0.003
0.005
0.4
0.004
0.006
0.9
0.014
0.015
scSplit,.s
0.9
0,003
0.003
0.4
0.003
0.005
0.7
0.015
0.014
scSplit
0,002
0.002
0.7
0.003
0.006
0.011
0.016
scSplit
0.002
0,002
0.003
0.005
0.6
0.011
0.014
U-Net
0.7
0.002
0.002
0.7
LLOCE
0.002
0.5
0.008
0.007
sSplit,
0.004
0.002
0.6
0.005
0.002
0.5
0.010
0.007
xSplit p
0.7
0.003
0.002
0.7
0.005
0.002
0.5
0.009
0.007
pSplitp
0,004
0.002
0.7
0.005
0.002
0.009
0.007
HTT24
denoiSplit
0.003
0.004
0.6
0.004
0.003
0.5
0.006
0.007
MicroSplit
0.7
0.003
0.004
0.7
0.004
0.003
0.5
0.007
0.007
InD1
0,002
0.003
0.6
0.003
0.002
0.006
0.005
sc0plitg.
0.6
0.001
0.001
0.6
0.003
0.001
0.5
0.005
0.007
scSplit
0.8
0.002
0.000
0.7
0.003
0.001
0.6
0.005
0.003
scSplit
0.001
0.000
0.6
0.002
0.001
0.6
0.005
0.003
U-Net
0.3
0.002
0.001
0.3
0.004
0.001
0.3
0.006
0.002
sSplit,
0,002
0.001
0.3
0.004
0.001
0.006
0.002
pSplitz
0.002
0.001
0.3
0.004
0.001
0.2
0.007
0.002
1Split
0.3
0.003
0.002
0.3
0.005
0.002
0.3
0.007
0.002
PaviaATN
denoiSplii
0.005
0.001
0.002
MicroSplit
0.1
0.004
0.001
0.1
0.004
0.001
0.1
0.004
0.001
InDI
0.2
0.001
0.001
0.1
0.003
0.001
0.1
0.005
0.002
scoplit
0.001
sc0plit
0.2
0.001
0.001
0.3
0.003
0.002
0.2
0.004
0.003
scSplit
0.2
0.001
0.000
0.3
0.003
0.002
0.2
0.004
0.003
Table S.10: Standard error values for Table 1 (channel-averagedd)
S.26

---

pSpli g
denoriSptit
S-plii 5
Tirget
Panto
PSMR
Paks 36.
PON 2033
POMR
POUR 24.7
Inpot
p-pllt
denoiSeel
1-5plit
SeSplit
Target
PSRR: 32.
PONT:363 26.5
PS4R: 30.
PSRR 10.3
Figure S.20: Qualitative evaluation superimposed raw microscopy images from HTLIF24 dataset. In each panel, we show the full input frame (top-left) and the zoomed-in in input patch (bottom-leti for which we show the predictions and the targets (last col) for the two channels, one in each row. We also report PSNR values for the patch shown.
pppli
denoiSplit
pSplit
Tirget
POR 29.9
2013
ParR: 2033
PSN
2548-263
PSRR 26.7
Inpor
pSpli
denoiSplit
A-plic 5
scSplit
Turget
PARA:
PARR
PAN 275
PON
2548-302
PSM 27.3
Figure S.21: Qualitative evaluation for superimposed raw microscopy images from HTT224 dataset, In each frame (top-left) and the zoomed-in input patch (bottom-lcft) for which we show the predictions and the targets (last col) for the two channels, one in cach row. We also report PSNR values for the patch shown.
panel, we show the input
S.27


Reviews:
[{"review_id": "14mWxJ7HHm", "reviewer": "Reviewer_n12V", "summary": "This work introduces a new method, indiSplit, to recover probe-specific signals from fluorescence microscopy images in which two signals have been mixed. Such digital demultiplexing methods could overcome technical limitations in fluorescence microscopy, by allowing for effective “overloading” of individual channels with multiple (instead of just one) structure-specific probes, thereby increasing the number of cellular structures that can be captured and cleanly related through multiplexed image acquisition pipelines. In a well-structured paper, the authors present the roots of their method, introduce technical modifications, and empirical evidence across several relevant datasets, along with numerous technical controls, that generally support their merit. However, certain methodological aspects remain unclear, one key ablation is missing, and the practical significance of indiSplit may be modest.", "questions": "1. To address weakness (1), I would ask that the authors address the relationship of the normalization module to instance norm / intrinsic normalizations of $c_t$ should be added. \n2. Weakness (3) could be addressed by adding sufficient detail to the text or appendix to clarify the extent to which indiSplit is iterative. \n3. The authors should affirm that InDI was faithfully implemented, i.e. as an iterative system. If not, the authors should clearly highlight this (including changing the acronym), and further explicitly delineate how indiSplit is different from their InDI implementation.   \n4. Depending on the difference between InDI and indiSplit, the authors should consider extending ablation experiments (weakness (2)) around the normalization question to other baselines. For example, for baselines trained by the authors, and in particular for InDI, instance norm of $c_t$ (a very cheap operation) could be explored.   \n5. If the authors could provide additional empirical data on the extent to which indiSplit generalizes to real images, ideally collected under relevant potential out-of-distribution settings (i.e. different technical circumstances such as a different microscope), that could substantially strengthen the significance of the work.   \n\nI expect addressing most of these key weaknesses to be feasible, and I would gladly increase my scores in response. I further extend my sincere apologies to the authors for the late submission of this review.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 1, "originality": 3, "strengths_and_weaknesses": "**Strengths:**  \n\n1. **A well-presented paper:** The authors present indiSplit in a well-written manuscript, with high-quality figures that clearly communicate motivation, reasoning, experimental design and results. Conclusions are well-calibrated to the level of empirical evidence provided.  \n2. **Clear application target:** The method has a clear real-world potential to address a concrete limitation in fluorescence microscopy, one of the most foundational and widely used techniques in biomedical research.  \n3. **High degree of experimental rigor:** Experimental include relevant technical controls which benefits attribution of empirical improvements to their method.  \n\n**Weaknesses:**  \n\n1. **Normalization module vs instance norm:** While the authors reasoning for the normalization module is clear, and the implementation effective, it appears that, to ensure $σ^2=1$ for input images during training, instead of precomputing a statistical memory bank, the same effect could be trivially achieved by applying instance normalization (i.e. using intrinsic statistics for normalization) to any input $c_t$ on the fly. If there are compelling technical reason against this, they should be discussed and empirically validated. While the use of instance normalization is well-established in computer vision, and in particular for fluorescence microscopy applications in which absolute intensity variations between technical replicates is assumed to be a major source of noise (e.g. cellular profiling [1]), documenting its empirical benefit in this context would still be useful. \n\n2. **Ablation of normalization module is missing:** Experiments to delineate the specific impact of ensuring $σ^2=1$ for any $c_t$ (as opposed to the impact of the time regressor module) are missing. \n\n3. **Unclear to what extent indiSplit is iterative:** The authors explain their study as building upon “InDI: Image Restoration by Direct *Iteration*” [2], but it remains unclear to what extent indiSplit, as well as the authors implementation of InDI for that matter, actually implements an iterative process of image of image restoration. This seems rather significant, because InDI’s primary innovation is exactly the iterative, stepwise recovery of source images in ill-posed settings. Method, experimental, and Appendix provide no information on this regarding indiSplit; Fig. 1 seems to show a one-shot restoration process. Moreover, the use of the Reg network seems more compatible with a single step of inference. In InDI, models learn to restore images over a consistent number of steps N, i.e. t=1 is implicitly set for any input image during inference and the image is restored over N steps of size δ. If indiSplit is indeed iterative in this sense, then it would seem that for any estimated $t_{agg}$<1, either N or δ would need to be adjusted dynamically. Whether or how this is done is unclear. \n\n4. **Generalization seems uncertain:** While indiSplit outperforms a strong set of baselines by substantial margins over datasets in which channels are artificially mixed, no clear performance advantage is apparent for real images. Combined with the fact that indiSplit seems to require two task-specific models to be trained for any particular unmixing setup (i.e. models trained to unmix some channels 1 and 2 are not expected to work for channels 1 and 3), and that these may well fail to generalize to images (with matched probes) collected on difference microscopes, the practical significance of indiSplit will likely be modest.   \n\n5. **Minor weaknesses:** There are some minor spelling mistakes. The authors may further want to sharpen their description of the distinction of natural vs. fluorescence microscopy images with respect to their value-distributions / histograms. In particular, the sentence in line 128 “For instance, it is common to have the maximum pixel intensity for a noisy acquisition to be less than where as [spelling mistake] the pixel intensities can easily be larger than 4000 for less noisy acquisitions.” should be refined to take account of varying image bit-depths (often 8-bit for natural images, hence dividing by 255 makes sense, but commonly 12- or 16-bit for microscope cameras).    \n\n[1] Pernice, W.M., Doron, M., Quach, A., Pratapa, A., Kenjeyev, S., De Veaux, N., Hirano, M. and Caicedo, J.C., 2023. Out of distribution generalization via interventional style transfer in single-cell microscopy. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 4326-4335).  \n[2] Delbracio, M. and Milanfar, P., 2023. Inversion by direct iteration: An alternative to denoising diffusion for image restoration. arXiv preprint arXiv:2303.11435.", "was_revised": true, "final_justification": "Over an extensive and indeed rather collaborative rebuttal period, the authors have provided many critical clarifications along with a substantial set of additional experiments. \n\n- In particular, it became clear that the proposed **normalization approach** had not been adequately described in the original manuscript. It also appears that, as per additional results produced by the authors in response to *Weakness 1*, the same effect can be achieved through a well-known approach, i.e. by applying Instance Normalization (IN), even though there may be subtleties with respect to how IN interacts with the proposed Reg module. The authors affirm that they will thoroughly revise Section 3.2. to account for the substantial gaps in formalism and to incorporate their results in IN. While these gaps could well have led to me downgrading my evaluation, I (1) trust that the corrections we have discussed will be implemented, and (2) note that the empirical results that normalization of $C_t$ (by one method or another) helps stand regardless (further supported by additional ablations), based on which I expect such normalization to become default practice in this application domain. \n\n- The authors have **clarified that the method is not iterative in nature**; the method will thus be renamed to scSplit, references to time / removed, and variable name $t$ changed accordingly. \n\n- Finally, we managed to figure out what the images in Table 2 actually correspond to, i.e. that they are indeed \"real enough\" to count as **a reasonable test of generalization of scSplit to non-synthetic images**. Relevant methodological details will be added to the paper. Generalization to actual application relevant images, and beyond that, to independent test data (OOD), remains unclear. This may be because suitable datasets are not available to the authors, but it's a limitation nonetheless, which compounds with the need to train probe-set specific models for every intended application.   \n\nAs such, the paper has been clearly improved: **The paper represents a technically meaningful step forward, even as limitations regarding the practical significance of the method remain.**", "rebuttal": "**Weaknesses:**\n\n1. *Normalization module vs instance norm:* \n    \n    **Answer:** The reviewer rightly pointed out that applying instance normalization (IN) in the first layer can, in principle, also mitigate the normalization issue we discovered for the semantic unmixing task. However, we have both empirical and domain-specific reasons to prefer our approach. \n\n     To evaluate this, we conducted experiments on the Hagen et al. dataset using instance normalization. We trained two additional baselines: (1) InDI (firstIN), with instance normalization as the first layer, and (2) InDI (allIN), replacing all group normalization layers with instance normalization plus a first-layer instance normalization. Similar variants were also created for the indiSplit network. Results (below) show our original indiSplit model outperforms most baselines. Notably, the 'firstIN' variant performs better than the 'allIN' variant. Results for the PaviaATN task with 'firstIN' are also reported in which case as well, indiSplit has clear out-performance for the bleedthrough regime (Dom.) and is competitive in others.\n\n|Dataset|Model|PSNR|SSIM|LPIPS|PSNR|SSIM|LPIPS|PSNR|SSIM|LPIPS|\n|-----------|-----------------|-|-|-|-|-|-|-|-|-|\n||||Dom. |||Bal.|||Weak.|\n|Hagen et al.|inDI(allIN)|36.5|0.987|0.026|32.4|0.968|0.060|27.9|0.914|0.132|\n|Hagen et al.|inDI(firstIN)|36.7|0.987|0.032|33.5|0.974|0.052|26.6|0.881|0.154|\n|Hagen et al.|indiSplit(allIN)|36.6|0.988|0.025|32.4|0.967|0.061|27.9|0.916|0.131|\n|Hagen et al.|indiSplit(firstIN)|40.1|0.993|0.016|**34.0**|0.976|0.051|29.0|0.924|0.129|\n|Hagen et al.|indiSplit|**40.9**|**0.994**|**0.011**|33.9|**0.977**|**0.046**|**29.3**|**0.934**|**0.123**|\n||\n|PaviaATN|inDI(firstIN)|28.8|0.950|0.102|27.1|0.903|**0.150**|21.3|0.768|**0.248**|\n|PaviaATN|indiSplit(firstIN)|33.5|0.975|0.042|**27.7**|0.906|0.172|**24.8**|**0.825**|0.440|\n|PaviaATN|indiSplit|**35.1**|**0.977**|**0.033**|27.6|**0.907**|0.155|24.3|0.823|0.377|\n\nFrom a technical perspective, when normalization is performed acquisition-wise—as we do during inference—rather than patch-wise (instance normalization), it equally accounts for the variability in pixel values observed in microscopy data caused by different acquisition settings. At the same time, this approach allows us to avoid the drawbacks associated with instance normalization. Instance norm has been reported to degrade discriminative performance in tasks where intensity clues or instance specific contrast is relevant [I,II]. In microscopy, intensity cues are important. For instance, the background can be easily distinguished from the 'content-less' interior of an organelle like nucleus simply by comparing average intensity value. However, instance norm can make it difficult as it normalizes per patch. This will be more true for smaller patch sizes, typically used for semantic unmixing (patch size of 64 and 128 were used by uSplit [3] and denoiSplit [2] respectively).  \n\n[I] Hyeonseob Nam, Hyo-Eun Kim. Batch-instance normalization for adaptively style-invariant neural networks. (NIPS'18). \n\n[II] Dmitry Ulyanov, Andrea Vedaldi, Victor Lempitsky. Improved Texture Networks: Maximizing Quality and Diversity in Feed-forward Stylization and Texture Synthesis. CVPR 2017.\n\n\n\n2. *Ablation of normalization module is missing:*\n    \n     **Answer:** We have now conducted the requested ablation study where the indiSplit model was trained without applying our custom normalization method. Instead, we used the commonly adopted approach in iterative inference models like InDI, where the two images are normalized first using mean-std normalization and then combined via a convex combination to form the intermediate input $ x_t $. Below, we present the results of indiSplit using this 2-image normalization scheme across four datasets. For each task, we trained the Reg and $Gen_i$ networks under this normalization approach. Across all tasks and all input regimes, it is evident that the PSNR values of the original indiSplit model (as reported in Table 1 of the main manuscript) outperform those reported here, with the sole exception of the task on PaviaATN dataset under the dominant input regime, where the PSNRs are equal.\n|Model|PSNR|SSIM|LPIPS|PSNR|SSIM|LPIPS|PSNR|SSIM|LPIPS|\n|------|-|-|-|-|-|-|-|-|-|\n|||Dom. |||Bal.|||Weak.|\n|PaviaATN|35.1|0.978|0.032|25.9|0.895|0.202|23.7|0.813|0.492|\n|Hagen|39.4|0.990|0.017|30.8|0.962|0.067|27.8|0.923|0.120|\n|HTT24|42.7|0.992|0.003|37.1|0.973|0.011|33.7|0.934|0.034|\n|BioSR|39.3|0.979|0.017|33.6|0.936|0.059|28.1|0.874|0.146|\n\n3. *Unclear to what extent indiSplit is iterative:*\n    \n    **Answer:** Our implementation of InDI is exactly as mentioned in the InDI paper [22], and therefore has the possibility of doing iterative inference with any number of steps (see  line 240 in model/ddpm_modules/joint_indi.py, given in supplementary.zip). \n    \n    However, in the Figure 3 of InDI paper, its authors quantitatively show that more iterations lead to worse PSNR (higher distortion) but improved perceptual quality. When working with predictive models on biological data, one can argue that in the perception-distortion tradeoff [I], the motivation is to get the model with a better fidelity to the recorded image (lower distortion). This would not be true if the motivation was to generate synthetic datasets, in which case better perceptual quality might be the major goal. With a focus on better fidelity,  we use one step prediction for both InDI and inDiSplit. \n    \n    Note that training in InDI is not iterative and so this choice does not affect in any way how InDI is trained. \n    \n    Finally, we chose InDI as the basis for our work not because of its ability to also be used iteratively, but due to its fitting inductive bias, i.e. the fact that the convex combinations of source and target images coincides perfectly well with the superposition of two differently intense structures being labeled in a single image channel on a fluorescence microscope. (For more details, see L92-L100 in the main manuscript). \n    \n    That all being said, iterative inference in indiSplit can done in the following way: Instead of starting from $t=1$ as done in InDI, one needs to start from the value of $t$ estimated with $Reg$ network. $\\Delta$, the unit decrement in $t$, can simply be computed as $\\Delta =t_{start}/totalSteps$. This is implemented in code (see line 93 in model/ddpm_modules/indi.py, given in supplementary.zip). The only other change that needs to happen is to ensure that $E[\\mu(x_t)] =0$ and $E[\\sigma(x_t)]=1$, where $\\mu()$ and $\\sigma()$ represents the mean and the standard deviation operators. This can easily be achieved by a normalization step in each step of the iterative inference. However, we do not focus on iterative generation in this work since it is not helpful in the context of the application use-case, where we clearly want, as described above, minimal distortion (maximum data fidelity). If the reviewer continues to consider indiSplit distinct from inDI, we would be glad to rename it to scSplit (severity cognizant split) or any other name the reviewer suggests.\n   \n[I] Y. Blau and T. Michaeli,The Perception-Distortion Tradeoff, CVPR 2018.\n\n\n4. *Generalization seems uncertain:*\n    \n     **Answer:** We believe that the results on real superimposed images were seen in a different light by the reviewer. Here, we present our point of view, and also show an additional experiment with real inputs to further prove our point. \n\n   **Why we are happy with Table 2:** The HTT24 and HTLIF24  datasets we used contains real inputs with balanced mixing ratios ((Line 206, main manuscript), as they were generated in MicroSplit [5] whose focus was not on asymmetric mixing. We see indiSplit’s strong performance within this balanced mixing-ratio range—where baselines were designed to excel—as a positive indicator of its versatility across mixing ratios.\n\n     **An additional experiment:**  We conducted an experiment demonstrating that indiSplit outperforms baselines when the relative strengths of structures in real superimposed input differ from those in synthetic sums. Using the HT-T24 dataset, we created two dataset variants by multiplying all pixel values in one structure channel by 4. So, the first channel is brighter than the second channel in the first dataset variant. The case is opposite for the second dataset variant. Using each variant, indiSplit and top two baselines (U-Net for LPIPS, denoiSplit for PSNR) for this dataset were trained and evaluated on the (unchanged) real superimposed images. Results presented below shows that IndiSplit consistently outperformed both baselines on both variants by a large margin in PSNR, showing robustness to changes in relative structure strength.\n\n|Model|Dataset|PSNR|SSIM|LPIPS|\n|------|--|-|-|-|\n|UNet|HTT24(4:1)|30.1|.906|.074|\n|denoiSplit|HTT24(4:1)|28.8|.854|.096|\n|indiSplit$_{0.5}$|HTT24(4:1)|32.3|.914|.069|\n|indiSplit($t_{agg}=0.82$)|HTT24(4:1)|**35.8**|**.956**|**.020**|\n||\n|UNet|HTT24(*1:4*)|28.5|.878|.109|\n|denoiSplit|HTT24(*1:4*)|30.3|.920|.115|\n|indiSplit$_{0.5}$|HTT24(*1:4*)|32.3|.927|.067|\n|indiSplit($t_{agg}=0.25$)|HTT24(*1:4*)|**35.6**|**.955**|**.020**|\n \n   **Generalizability across structure types:** We acknowledge the reviewer’s point that models trained to unmix channels 1 and 2 may not generalize to channels 1 and 3. However, given the early stage of research, this is less critical. Semantic unmixing is still nascent, with only two deep-learning methods (uSplit , denoiSplit ) published in top computer vision/ML venues—both using synthetic mixes. MicroSplit, recently uploaded to arXiv, is the only work addressing real superimposed images.\n    \n\n5. *Minor weaknesses:* \n    \n    **Answer:** We thank the reviewer for his comment. We will spend time to fix all typos."}, {"review_id": "3O611Q5tqa", "reviewer": "Reviewer_qCeF", "summary": "The authors introduce **indiSplit**, a novel computational method for fluorescence microscopy image decomposition, specifically designed to handle unknown mixing ratios between channels in multiplexed images. The paper proposes a potentially useful method, but I have significant doubts about its evaluation methodology due to reliance on metrics suited for different tasks and unrealistic test data derived from blending itself.", "questions": "Are the metrics you used adequate to achieve unmixing? Can you propose another metric that would measure that, for example, a downstream segmentation metric?", "limitations": "Please clearly describe the practical problem that the task you are interested in is supposed to solve. Mention limitations of the metrics in assessing how well the task is addressed. Mention clearly how practical the datasets are that you are using to train and test the model. What are the limitations?", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe paper builds upon an existing technique by adding a regressor network that predicts the severity of the mixing ratio and a normalisation module based on this prediction, allowing degradation-aware splitting and bleed-through removal across various intensity conditions.\n\nMajor Weaknesses:\n\n1. The paper primarily uses standard image quality metrics like PSNR (Peak Signal-to-Noise Ratio), SSIM (Structural Similarity Index), and LPIPS (Learned Perceptual Image Patch Similarity). However, these metrics fundamentally assess how closely an output resembles a specific *target* image. As a result, the authors do not measure **channel separation** effectively. The task requires direct bleed-through reduction in the biological signal, which is not represented in any of the datasets used. The task should be measured by how accurately the models are unmixing overlapping signals to reveal distinct cellular structures and quantify markers independently. PSNR/SSIM/LPIPS fail to capture this because these metrics measure quality and therefore bear secondary importance.\n\n2.  The evaluation was performed on synthetic blended image datasets, which do not reflect the reality of unmixing unknown bleed-through from actual experimental acquisitions with variable intensities. This is likely an unrealistic assessment of performance in a real-world microscopy context where mixing ratios are unpredictable.\n\n3.  It's unclear why absolute pixel values (as opposed to relative signal contributions or normalised intensity) are used as the basis for\nevaluation, given their potential variability due to acquisition settings. In microscopy, raw intensity levels depend heavily on acquisition settings and can fluctuate naturally.", "was_revised": true, "final_justification": "I have updated my score following the discussion. However, by authors' own admission, certain limitations such as the necessity to retrain the model for each individual dataset and the inability to tackle artefacts still persist.", "rebuttal": "## Major Weaknesses:\n\n1. *The paper primarily uses standard image quality metrics like PSNR, SSIM, and LPIPS. However, these metrics fundamentally assess how closely an output resembles a specific *target* image. As a result, the authors do not measure **channel separation** effectively. [...] PSNR/SSIM/LPIPS fail to capture this because these metrics measure quality and therefore bear secondary importance.*\n    \n    **Answer:** We thank the reviewer for this question which has three very relevant enquiries for fluorescence microscopy.  We answer them in different paragraphs.\n    \n    **Suitability of metrics used for semantic unmixing task:** Previous methods developed for semantic unmixing—such as uSplit [3], denoiSplit [2], and MicroSplit [5]—have all used PSNR and SSIM variants. In line with this, we also report these metrics. While LPIPS, and to some extent SSIM, reflect perceptual quality (which the reviewer refers as 'quality') rather than distortion, PSNR is especially appropriate here, as it quantifies pixelwise error. Moreover we use the range invariant version of PSNR [28] which was developed precisely for microscopy data to compare prediction on a low SNR image (low pixel values) against a high-SNR groundtruth. The SSIM variant we use, was also developed for microscopy [29]. Nonetheless, we also present segmentation results later in our response.\n    \n    **Tasks not matching bleedthrough-removal**: Owing to space limitations, we were unable to include qualitative examples of bleed-through removal in the main manuscript. We invite the reviewer to consult the supplementary figures (starting from Figure S4), where qualitative plots for each dataset are presented across all mixing levels. These figures illustrate numerous instances where faint structures visible in the input are successfully removed.\n    \n    **Suitability of metrics for bleedthrough-removal task:** We acknowledge that, because bleed-through represents a minor unwanted signal, even input-to-target comparisons will yield relatively high metric values. To address this, we had included an “Input vs. Target” row in Table 1 showing the metric comparison between the target and input. Additionally, the fact that metric values are higher in this setting does not pose an issue, as all baselines are affected similarly; the approach achieving superior performance will continue to deliver better metric values.\n    \n2. *The evaluation was performed on synthetic blended image datasets, which do not reflect the reality of unmixing unknown bleed-through from actual experimental acquisitions with variable intensities....*\n    \n    **Answer:** In the following paragraphs, we present our three key responses: (a) the usefulness of synthetically blended semantic unmixing, (b) our work involving real superimposed images, and (c) an additional experiment conducted with real superimposed images, showcasing generalizability of indiSplit to different mixing-ratios.\n  \n   **Synthetically blended semantic unmixig is useful:** In Supplementary Section C.3 of Microsplit [5] , the authors evaluated the performance impact of training a semantic unmixing model using synthetically summed inputs, then testing it on real acquired inputs. They found that the performance drop was not detrimental. Furthermore, we have consulted with several microscopists about using real microscopy images as targets and their sums as inputs. Since superposition in fluorescence microscopy is indeed linear [19–21], microscopists—although naturally preferring real superimposed images—generally agree with us in the use of synthetically summed inputs derived from real target channels.\n    \n    **Results on real superimposed images**: In Table 2 of the main manuscript, we report results on real superimposed images; however, these correspond to the balanced input regime, where the input contains roughly equal contributions from both structures (Line 206, main manuscript), which is not an ideal dataset for this work. To date, there is no publicly available dataset that fits our use case, which requires both individual target channels and corresponding superimposed input images with varying mixing ratios. Consequently, using synthetic sums remains the only practical approach currently available to study variable mixing ratios. However, we did an experiment to show the generalizability of indiSplit across different mixing-ratios, which we describe next.\n\n   **An additional experiment with real inputs:**  We conducted an experiment demonstrating that indiSplit outperforms baselines when the relative strengths of structures in real superimposed input differ from those in synthetic sums. Using the HT-T24 dataset, we created two dataset variants by multiplying all pixel values in one structure channel by 4. So, the first dataset variant, named HTT24(4:1), has its first channel multiplied by a factor of 4, and therefore is brighter than the second channel. In the second dataset variant, named HTT24(1:4), the second channel is brighter. Using each variant, indiSplit and top two baselines for this dataset (U-Net for LPIPS, denoiSplit for PSNR) were trained and later evaluated on the (unchanged) real superimposed images. Note that the training did not use real superimposed images. We report the evaluation on real superimposed images below, which shows that IndiSplit consistently outperformed both baselines on both variants by a large margin in PSNR, showing robustness to changes in relative structure strength.\n\n|Model|Dataset|PSNR|SSIM|LPIPS|\n|-|-|-|-|-|\n|UNet|HTT24(4:1)|30.1|.906|.074|\n|denoiSplit|HTT24(4:1)|28.8|.854|.096|\n|indiSplit($t_{agg}=0.82$)|HTT24(4:1)|**35.8**|**.956**|**.020**|\n||\n|UNet|HTT24(*1:4*)|28.5|.878|.109|\n|denoiSplit|HTT24(*1:4*)|30.3|.920|.115|\n|indiSplit($t_{agg}=0.25$)|HTT24(*1:4*)|**35.6**|**.955**|**.020**|\n \n3. It's unclear why absolute pixel values (as opposed to relative signal contributions or normalised intensity) are used as the basis for evaluation, given their potential variability due to acquisition settings. In microscopy, raw intensity levels depend heavily on acquisition settings and can fluctuate naturally.\n    \n    **Answer:** In fluorescence microscopy images, there is considerable variability in pixel intensity levels across different acquisitions due to varying acquisition settings. However, this variability does not impact our work since we do not perform comparisons across different datasets; each model is trained and evaluated on the same dataset split. Moreover, evaluating in a normalized space allows for the possibility of using different normalization methods, which can lead to variations in metric values for the same prediction. This may pose challenges for future studies attempting to directly compare or cite our metric results.\n\n## Questions\n1. *Are the metrics you used adequate to achieve unmixing? Can you propose another metric that would measure that, for example, a downstream segmentation metric?*\n\n   **Answer:** Regarding the suitability of metrices used by us, please see our answer to Major weakness no. 1. We agree with the reviewer that improved metrics would be beneficial and not much work has been done to design metrics specifically for microscopy data. However, every metric has its limitations. While segmentation could be used to assess quality, it overlooks the relative intensity variations within a labeled object. Since our predictions involve continuous pixel values rather than just two discrete classes (foreground and background), segmentation alone cannot fully capture the quality of the prediction. For example, a method producing artifacts within a labeled object might still receive a similar ranking to a method without such artifacts, as segmentation may fail to detect these subtle errors.\n\n    That said, for the bleed-through removal task (w=0.7, 0.8, 0.9), we have now used the test set of BioSR dataset to evaluate segmentation as a downstream task with Featureforest (max_depth=9,numtrees= 450, encoder=SAM2_large), a recently developed segmentation method [I]. To avoid model bias, we manually annotated the ground truth and trained Featureforest using these annotations alongside model predictions (If we had annotated the predictions instead, it would raise concerns about the consistency and quality of annotations when doing it for indiSplit and for the baseline models). We trained $4 × 2 × 3 =24$ Featureforest models—one per model, channel, and mixing ratio. Evaluation used the Dice dissimilarity from scipy (lower is better). Among baselines, segmentations from indiSplit predictions best matched those of the ground truth channel, thereby perfectly correlating with PSNR based assessment. **We will add these segmentation-based evaluation results to the manuscript.**\n\n| Model               | .           | DICE | DISSIM. |  SCORE | ↓ | . |\n|-------------------|---------|--------|---------|--------|--------|-------|\n| .                        |             | Ch0    | .          | .         | Ch1    | .        |\n| .                        |w=0.7.  | w=0.8 |w=0.9  |w=0.7 |w=0.8. |w=0.9|\ndenoiSplit           | 0.077   | 0.073 | 0.065  | 0.064  | 0.061 | 0.056 |\n$\\mu$Split$_D$ | 0.055    | 0.051 | 0.047  | 0.051 | 0.047 | 0.038 |\nInDI                     | 0.055.  | 0.05   | 0.044  | 0.046  | 0.045 | 0.045 |\nindiSplit              | **0.048** | **0.039** | **0.035** | **0.038** | **0.032** | **0.026** |\n\n[I] Seifi et al. FeatureForest: the power of foundation models, the usability of random forests. npj Imaging 3, 32 (2025). https://doi.org/10.1038/s44303-025-00089-9\n\n## Paper Formatting Concerns:\n\n*Figures in the paper are missing standard elements like channel names and scale bars, which is unusual for scientific image publications.*\n\n**Answer:** We thank the reviewer for bringing to our attention missing scale bars and channel names. We will certainty update them."}, {"review_id": "wwZdrpb4of", "reviewer": "Reviewer_ggcu", "summary": "This article addresses the issue of limited observable cell structures in a single fluorescence microscopy image and proposes a method named indiSplit by introducing a regression network to predict mixing proportions and a degradation-specific normalization module. This method solves the tasks of image decomposition and crosstalk elimination, with its effectiveness validated on multiple public datasets.", "questions": "1. The input image c_t is generated by linearly superimposing two structural images c_0 and  c_1  with a mixing proportion t in [0,1] , i.e.,  c_t = (1-t)c_0 + tc_1. Why is the superposition implemented as an addition here? Typically, superposition often involves multiplying two textures.  \n2. Has the author conducted experiments to prove that different mixing proportions significantly affect the results?  \n3. Is the method applicable to multi-layer superposition?  \n4. If interference occurs between superimposed textures, does the method in the article remain applicable?  \n5. It is recommended to split the performance comparison in Table 1 and the model's research on mixing parameters into two separate tables.", "limitations": "Please refer to my questions part.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "### Strengths  \nThe article primarily introduces two modules: mixing ratio perception and degradation-specific normalization. Through a regression network and an aggregation module, the method explicitly models the changes in superimposed intensity, addressing the limitation of traditional methods that assume a fixed mixing ratio. Normalization is employed to ensure consistent input data distribution under different mixing proportions.  \n\n\n### Weakness  \nPlease refer to my detailed comments.", "was_revised": true, "final_justification": "My questions and concerns have been addressed, and I will update my final rating to borderline accept.", "rebuttal": "## Questions\n\n1. *The input image c_t is generated by linearly superimposing two structural images c_0 and c_1 with a mixing proportion t in [0,1] , i.e., c_t = (1-t)c_0 + tc_1. Why is the superposition implemented as an addition here? Typically, superposition often involves multiplying two textures.*\n    \n    **Answer:** In fluorescence microscopy, superposition of structures is linear [18-21]. Previous deep-learning based works like uSplit [3] and denoiSplit[2], published in International Computer Vision conferences, also work with the above mentioned weighted average formulation.  \n    \n2. *Has the author conducted experiments to prove that different mixing proportions significantly affect the results?*\n    \n    **Answer:** There are two potential ways in which different mixing proportions can affect results. \n    \n    (a) One way is that the prediction quality for the less represented channel is poorer. This trend appears consistently across all rows of Table 1, where metrics are highest for the Dominant input regime, followed by the Balanced regime, and lowest for the Weak regime. The test set’s underlying structures remain unchanged across these regimes; only the input mixing ratios vary. For instance, given two images $ c_1 $ and $ c_2 $, an input is formed as $x = 0.1 c_1 + 0.9 c_2 $. We trust the reviewer would agree that predicting $ c_2 $ from $ x $ is easier than predicting $ c_1 $, since $ c_2 $ is more prominently represented in the input.\n    \n    (b) The second is that if the network was accustomed to train on a specific mixing-ratio, then, at inference time, deviation from that mixing-ratio would lead to inferior results. For this, we conducted an experiment demonstrating that indiSplit outperforms baselines when the relative strengths of structures in real superimposed input differ from those in synthetic sums. Using the HT-T24 dataset, we created two dataset variants by multiplying all pixel values in one structure channel by 4. So, the first dataset variant, named HTT24(4:1), has its first channel multiplied by a factor of 4, and therefore is brighter than the second channel. In the second dataset variant, named HTT24(1:4), the second channel is brighter. Using each variant, indiSplit and top two baselines for this dataset (U-Net for LPIPS, denoiSplit for PSNR) were trained and later evaluated on the (unchanged) real superimposed images. Note that the training did not use real superimposed images. We report the evaluation on real superimposed images below, which shows that IndiSplit consistently outperformed both baselines on both variants by a large margin in PSNR, showing robustness to changes in relative structure strength.\n\n\n|Model|Dataset|PSNR|SSIM|LPIPS|\n|------|--|-|-|-|\n|UNet|HTT24(4:1)|30.1|.906|.074|\n|denoiSplit|HTT24(4:1)|28.8|.854|.096|\n|indiSplit$_{0.5}$|HTT24(4:1)|32.3|.914|.069|\n|indiSplit($t_{agg}=0.82$)|HTT24(4:1)|**35.8**|**.956**|**.020**|\n||\n|UNet|HTT24(*1:4*)|28.5|.878|.109|\n|denoiSplit|HTT24(*1:4*)|30.3|.920|.115|\n|indiSplit$_{0.5}$|HTT24(*1:4*)|32.3|.927|.067|\n|indiSplit($t_{agg}=0.25$)|HTT24(*1:4*)|**35.6**|**.955**|**.020**|    \n\n\n3. *Is the method applicable to multi-layer superposition?*\n    \n    **Answer:** No, it is not. We plan to tackle semantic unmixing of more than two structures as part of our future work. \n    \n4. *If interference occurs between superimposed textures, does the method in the article remain applicable?*\n    \n    **Answer:** Interference is not a prominent problem in Fluorescence microscopy. Since fluorescence emission is broadband and incoherent, it reduces the possibility of forming stable interference patterns at the detector [I, II]. Moreover, fluorescence interferometry produces interference fringes only when fluorophores lie very close to a zero-differential path length—within the fluorescence coherence length of a few microns. Fluorophores beyond this range produce no interference pattern; the detector simply measures emission intensity [III]. Thus, typical fluorescence microscopy does not detect interference patterns unless specifically designed for interferometric imaging.\n    \n    [I] Bilenca A, Cao J, Colice M, Ozcan A, Bouma B, Raftery L, Tearney G. Fluorescence interferometry: principles and applications in biology. Ann N Y Acad Sci. 2008;1130:68-77. doi: 10.1196/annals.1430.038. PMID: 18596334; PMCID: PMC10902801.\n    \n    [II] Sanderson MJ, Smith I, Parker I, Bootman MD. Fluorescence microscopy. Cold Spring Harb Protoc. 2014 Oct 1;2014(10):pdb.top071795. doi: 10.1101/pdb.top071795. PMID: 25275114; PMCID: PMC4711767.\n    \n    [III] Bilenca A, Cao J, Colice M, Ozcan A, Bouma B, Raftery L, Tearney G. Fluorescence interferometry: principles and applications in biology. Ann N Y Acad Sci. 2008;1130:68-77. doi: 10.1196/annals.1430.038. PMID: 18596334; PMCID: PMC10902801.\n    \n5. *It is recommended to split the performance comparison in Table 1 and the model's research on mixing parameters into two separate tables.*\n    \n    **Answer:** We thank the reviewer for the comment. We will restructure the Table 1 appropriately."}, {"review_id": "Gl6SF9Ch7d", "reviewer": "Reviewer_Lyze", "summary": "This paper proposes a novel framework, indiSplit, to decompose fluorescence microscopy images containing mixed structures. The authors observe that in real-world scenarios, the mixing ratio of components can vary across images. To address this, they design a two-stage architecture: a Reg model estimates the mixing ratio, and a Gen model then predicts the individual components conditioned on this ratio. Additionally, an auxiliary normalization step is introduced to refine the mixed image, which originally has a variance as a function of the mixing ratio. The indiSplit framework outperforms prior approaches on relevant benchmarks and demonstrates potential generalizability to natural image tasks such as motion deblurring.", "questions": "1. Why was 100 chosen as the number of intervals in Section 3.2? Is this value optimal or empirically determined?\n\n2. Please address whether the two-stage pipeline is strictly necessary, or whether an end-to-end model with sufficient training data could perform equally well (related to Weakness 1).\n\n3. Can the model generalize to unseen combinations of component types, or does it require retraining for every new pair (related to Weakness 2)?\n\n4. Can you theoretically or empirically justify the proposed normalization strategy in inference? Given that ground truth is available in your experiments, use it to verify that your normalization leads to the desired variance behavior (related to Weakness 4).\n\n5. What is the precise meaning of t? Is it a mix ratio, a time variable, or both? Please clarify (related to Weakness 5).", "limitations": "The paper should clearly state that the current approach requires retraining when the types of mixed components change.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The idea of explicitly modeling the varying mixing ratios in composed images is novel and insightful for this task.\n\n2. The proposed normalization mechanism helps align the distribution of mixed images, which empirically improves performance.\n\n3. Decomposing the problem into two sub-tasks (mix ratio estimation and conditional generation) is a meaningful design choice and leads to improved separation quality.\n\nWeaknesses:\nMajor:\n1. It remains unclear why a single unified network could not implicitly learn the mixing ratio and perform separation directly. Typically, multi-stage pipelines are introduced when data scarcity limits end-to-end learning.\n\n2. The method appears to require retraining if the component types change. For example, if a model is trained to separate mixed types $C_0$ and $C_1$, can it generalize to mixed types $C_0$ and $C_2$? This raises concerns about generalizability and scalability.\n\n3. Related to the above, the framework lacks flexibility: different combinations of components require retraining the full model.\n\n4. The inference-time normalization using precomputed statistics indexed by the mean output of the Reg model is underexplained. If the input variance also depends on the mixing ratio, what is the theoretical basis for assuming this strategy leads to unit variance after normalization? A mathematical justification would be helpful.\n\n5. There is ambiguity around the meaning of t. While initially introduced as the mix ratio, Section 3.3 refers to t as time in the “Time Regressor Network Reg,” which is confusing and should be clarified.\n\nMinor:\n1. In the abstract, please clarify what is meant by \"technical limitations\" in the first sentence.\n\n2. Define the term superposition severity, as it is not a standard expression in the literature.\n\n3. Consider writing Bleedthrough in lowercase or using quotation marks to emphasize it.\n\n4. The introduction should explicitly mention that the proposed framework is inspired by InDI.\n\n5. In Section 3.2, specify the data type of the input images (e.g., uint16) to clarify the range and interpretation of pixel intensities.\n\n6. The definition of $C_i$​ appears redundant with the earlier definition of $C_0$​ and $C_1$.\n\n7. There is no definition provided for $\\delta$​; this should be clearly introduced.\n\n8. Please standardize the spelling of \"artifact\" vs. \"artefact\" throughout the manuscript.", "was_revised": true, "final_justification": "The authors have addressed all my concerns in the rebuttal. While the paper has a limitation in that retraining is required if a new combination is provided, the approach of splitting the process into two stages—first estimating the ratio, then separating—offers valuable insight in this field. Therefore, I maintain my original score of Borderline Accept.", "rebuttal": "## Weaknesses: Major:\n\n1. *It remains unclear why a single unified network could not implicitly learn the mixing ratio and perform separation directly. Typically, multi-stage pipelines are introduced when data scarcity limits end-to-end learning.*\n    \n    **Answer:** We concur with the reviewer that there is no fundamental conceptual obstacle to jointly training the Reg and the two Gen networks. However, due to practical constraints, e.g. GPU memory and/or network capacity and optimization difficulties for a joint setups, we chose the presented approach. This was further motivated by catering our work to microscopy labs, who are our future users, and typically are even more limited wrt. computational resources.\n    \n2. *The method appears to require retraining if the component types change. For example, if a model is trained to separate mixed types $C_0$ and $C_1$, can it generalize to mixed types $C_0$ and $C_2$? This raises concerns about generalizability and scalability.*\n    \n    **Answer:** We agree with the reviewer that one needs to retrain if the mixed structures (component types) change. Today, this is common practice for microscopy denoising and image restoration models, and we would always recommend training from scratch rather then reuse models “out of distribution”. \n    \n    Additionally, please note that semantic unmixing is a nascent field. To the best of our knowledge there are only two deep-learning based solutions published in international computer vision/ML conferences (uSplit [3] & denoiSplit [2]). Both of these works do not cater to different mixing ratio. In this work, we show that for both methods, asymetric mixing ratios are leading to problematic results (Table 1, main manuscript). Hence, while we are not suggesting generalizability to unseen structures, our work does help to generalize unmixing to a broader range of mixing ratios than any other method today is capable of.\n   \n3. *Related to the above, the framework lacks flexibility: different combinations of components require retraining the full model.*\n    \n    **Answer:** We agree with the reviewer that it will be amazing if such a flexible model is developed and does performs reliably, but the field is yet to develop one. Please see our previous answer for a longer discussion.\n    \n4. *The inference-time normalization using precomputed statistics indexed by the mean output of the Reg model is underexplained. If the input variance also depends on the mixing ratio, what is the theoretical basis for assuming this strategy leads to unit variance after normalization? A mathematical justification would be helpful.*\n    \n    **Answer:** Below, we provide both mathematical and empirical justification for our test-time normalization. \n    \n    Regrading the mentioned “precomputed statistics”, we want to ensure that there has not been any misunderstandings: The beauty of our training-time normalization method is that inference-time normalization becomes straightforward — one simply calculates the statistics (mean and standard deviation) from the sampled test-image patches, and then use those values for normalization. We will revise the text to make this critical point crystal clear for our future readers.\n    \n    **Theoretical Evidence:** In Supplementary Section A, we theoretically show that for images of size HxW, if one was to use iterative inference models such as InDI for semantic unmixing, the standard deviation of intermediate inputs $x_t$ would depend on the mixing ratio $t$. In this work, we have discussed the issues arising from this dependency. To remedy this, during training, we calculate the mean and standard deviation of intermediate input patches $x_t$ separately for each value of t, and use these statistics to normalize the $x_t$. Consequently, by design, the expected mean ($E[\\mu(x^{norm}_t)]$) and standard deviation ($E[\\sigma(x^{norm}_t)]$) of the normalized $x_t$ are 0 and 1, respectively, for all t. Therefore, at test time, it is sufficient for the input patches to have an expected mean of 0 ($E[\\mu(x^{norm})] =0$) and expected standard deviation of 1 ($E[\\sigma(x^{norm})] =1$), which is precisely what our inference-time normalization ensures. (Side note: for this argument to be water-tight, we assume that all test-data comes from a single acquisition and therefore has a single value of t.)\n    \n    **Empirical Evidence:** We have the empirical evidence in Supplementary Figure S19, where we show the average standard deviation of normalized input patches for $t \\in [0.1,0.2,…,0.9]$. We have, for each t, used 10k random input patches from the test dataset to compute the mean and standard deviation. We have then applied those statistics on 2000 other random input patches to get the average standard deviation of normalized input patches, showing that our proposed method leads to standard deviations concentrated around 1 for all mixing ratios t — which is exactly what we have aimed for. \n    \n5. *There is ambiguity around the meaning of t. While initially introduced as the mix ratio, Section 3.3 refers to t as time in the Time Regressor Network Reg, which is confusing and should be clarified.*\n    \n \n   **Answer:** We will clarify this in the final manuscript. While t is indeed the mixing ratio, it is also precisely the value the Reg network predicts. We propose to rename the 'Time Regressor Network Reg' to become the 'Mixing-ratio Network Reg'. By avoiding the word 'time', and adding a clear sentence making the connection between t in these two contexts, we believe future readers will be much less likely to be confused.\n\n\n\n## Raised minor points:\n\n**Answer:** We thank the reviewer for providing these comments. We will naturally incorporate all of them. The phrase 'Technical limiations' refers to excitation and emission spectra overlap, limited photon budgets and other factors which limits the maximum number of structures one can image concurrently in Fluorescence microscopy. \n\n\n## Questions:\n\n1. *Why was 100 chosen as the number of intervals in Section 3.2? Is this value optimal or empirically determined?*\n    \n    **Answer:** We chose the number of intervals based on the principle that the interval width should not exceed the error in estimating t using Reg. If it did, we would accept to reduce the mixing ratio granularity the Reg network is in principle capable of giving us. For example, in the HTLIF24 derived task, the mean absolute error (MAE) between the predicted and actual t values within the valid range $[0.1, 0.9]$ is 0.03 (see Supplementary Table S3, column 2). Therefore, any interval size smaller than 0.03 would be appropriate for this task. Following this reasoning, we selected a smaller interval size of 0.01—resulting in 100 intervals—to ensure the interval width remained sufficiently low across all tasks. \n    \n\n2. *Please address whether the two-stage pipeline is strictly necessary, or whether an end-to-end model with sufficient training data could perform equally well (related to Weakness 1).*\n   \n   **Answer:** See the answer to Major Weakness no. 1.\n\n    \n3. *Can the model generalize to unseen combinations of component types, or does it require retraining for every new pair (related to Weakness 2)?*\n \n   **Answer:** See the answer to Major Weakness no. 2.\n\n    \n4. *Can you theoretically or empirically justify the proposed normalization strategy in inference? Given that ground truth is available in your experiments, use it to verify that your normalization leads to the desired variance behavior (related to Weakness 4).*\n\n     **Answer:** See the answer to Major Weaknesses no. 4.\n\n    \n5. *What is the precise meaning of t? Is it a mix ratio, a time variable, or both? Please clarify (related to Weakness 5).*\n    \n     **Answer:** We will clarify in the camera-ready version, as mentioned in our response to Major Weaknesses no. 5."}]

Author rebuttal:

Meta-review: as all the reviewers decide to accept this paper, i recommend to accept this paper. however so many issues are discussed during the rebuttal phase. the authors should revise the paper based on the discussion.
Decision: Accept (poster)