FIPER: Factorized Features for Robust Image Super-Resolution and Compression
Authors: Yang-Che Sun
Cheng Yu Yeo
Ernie Chu
Jun-Cheng Chen
Yu-Lun Liu
Venue: NeurIPS 2025 poster ()
Keywords: Super-resolution
Image compression
Primary area: applications
TL;DR: An unified image representation to reconstruct the fine details.

Abstract: In this work, we propose using a unified representation, termed **Factorized Features**, for low-level vision tasks, where we test on **Single Image Super-Resolution (SISR)** and **Image Compression**. Motivated by the shared principles between these tasks, they require recovering and preserving fine image details, whether by enhancing resolution for SISR or reconstructing compressed data for Image Compression. Unlike previous methods that mainly focus on network architecture, our proposed approach utilizes a basis-coefficient decomposition as well as an explicit formulation of frequencies to capture structural components and multi-scale visual features in images, which addresses the core challenges of both tasks. 
 We replace the representation of prior models from simple feature maps with Factorized Features to validate the potential for broad generalizability.
 In addition, we further optimize the compression pipeline by leveraging the mergeable-basis property of our Factorized Features, which consolidates shared structures on multi-frame compression.
 Extensive experiments show that our unified representation delivers state-of-the-art performance, achieving an average relative improvement of 204.4\% in PSNR over the baseline in Super-Resolution (SR) and 9.35\% BD-rate reduction in Image Compression compared to the previous SOTA.

FIPER: Factorized Features for Robust Image Super-Resolution and Compression
Yang-Che Sun'
Cheng Yu Yeo'
Ernie Chu
Jun-Cheng Chen
Yu-Lun Liu' AAcademia Sinica
National Yang Ming Chiao Tung University
JJohns Hopkins University
Abstract
In this work, we propose using a unified representation, termed Factorized Fea- tures, for low-level vision tasks, where we test on Single Image Super-Resolution (SISR) and Image Compression. Motivated by the shared principles between these tasks, they require recovering and preserving fine image details, whether by enhancing resolution for SISR or reconstructing compressed data for Image Compression. Unlike previous methods that mainly focus on network architec- ture, our proposed approach utilizes basis-coefficient decomposition as well explicit formulation of frequencies to capture structural components and multi-scale visual features in images, which addresses the core challenges of both tasks. We replace the representation of prior models from simple feature maps with Factorized Features to validate the potential for broad generalizability. In addition, we further optimize the compression pipeline by leveraging the mergeable-basi property of our Factorized Features, which consolidates shared structures on multi- frame compression. Extensive experiments show that unified representation delivers state-of -ffe-h--rrttt performance, achieving an average relative improvement of 204.4% in PSNR over the baseline in Super-Resolution (SR) and 9.35% BD-rate reduction Image Compression compared to the previous SOTA. Project page: http:///ayiaaaaiingg.iuuuu.oo//o
1 Introduction
Single-image super-resolution (SISR) aims to recover high-quality images from low-resolution inputs, with accuracy depending on precise restoration of fine details and geometric correspondences (e.g., were followed by GAN-based methods for perceptual realism [47] and Transformer networks for long-range context [1]. Swin-based variants further boosted performance [22 I8 7I) inspiring ever-heavier architectures. These prior works optimize network design while neglecting the underlying image-content representations themselves. On the seek to model the frequency components directly through adding Fourier- or Wavelet-like bottlenecks the middle. Although these designs can indeed better capture the recurring visual patterns in learning effective SR representations than aforementationed methods, as illustrated in fig. [ they still suffer from poor perceptual quality.
stripes, grids, textures). CNN pioneers 24 39
other hand, decomposition- based methods [6
44
39
This raises a critical question: beyond simple network output, can we derive formulation that more effectively captures these patterns and aligns with the goals of SISR?
Conventional multi-scale pyramids aggregate features at several resolutions, but they store all acti- vations densely, do not disentangle frequency content, and cannot be shared directly across tasks. Instead, our factorized descriptor decomposes images into generalizable basis x coefficient pairs, providing explicit multi-frequency handle through different modulations.
On the other hand, image compression serves as a fundamental task in low-level vision applications, where the traditional compression standards [] 95 92 lay the groundwork. The emerging learned
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Figure 1: In this work, we propose represent images by Factorized Features, contrasting with prior methods that either (a) rely on fixed-basis decomposition [6]] (39 or (b) introduce various complex model blocks [IS 7 such as sparse attention, dense skip connection, etc. As highlighted in the orange boxes, (a) successfully captures periodic line structures but suffers from lower fidelity, while (b) cannot recover those repeating patterns without explicit frequency modeling. contrast, our method (c) uses learned decomposition with generalizable bases to deliver high-fidelity reconstruction while preserving periodic structures. We also present LAM [32] and Diffusion Index (DI) (32) for reconstructing the red-boxed patch, with its pixcl-importance map shown the middle row; a higher DI indicates more pixel utilization.
image compression models 88
3
34
62
80
compression algorithms of which mostly follow paradigm, then introduce a variety of networks 196 62]
20
the pixel-space transform coding 8 31
difference losses B55 further optimize compression efficiency by learning more compact latent representations and improving reconstruction quality. Specifically, they convert pixels into compact representations through transform module, which eliminates the redundancy and reduces the bit cost in the subsequent entropy coding process. However, the core challenge image compression is to accurately reconstruct the information lost during compression and quantization. In other words, the models can essentially be viewed as reconstructing a high-quality image from its 'low-resolution' version, much like Reper-Resoluttin all other common low-level vision tasks such as image restoration, deblurring, denoising, etc.
106 67 27
Based the aforementioned analysis, it becomes clear that although these tasks appear to be distinct, they share mutual similarities in two key aspects: (1) The tasks require models to restore fine details from low-quality image content, well implicitly capture and reconstruct repetitive structural elements. (2) They aim to conserve image quality, either by enhancing resolution or efficiently compressing data without significant loss of perceptual fidelity. Hence, inspired by recent advances in decomposition fields and matrices factorization in 3D scene modeling [1] 81 g 28 12 30).
propose unified representation, Factorized Features, with generalizable Coefficient Backbone and Basis Transformer for learned coefficient and basis, respectively. This approach explicitly captures multi-scale visual features and repetitive structural components in images through basis- coefficient decomposition. The resulting representation strikes a balance between being compact and information-rich, enabling the resolution of structural ambiguities and the precise modeling of image details through a multi- multi-frequency formulation.
Finally, also propose consolidating multiple bases into through network for multi-image processing, as in traditional Discrete Fourier Transform, all signals same size are reconstruct by the same set of basis functions, and argue that learned shared basis leverage the mutual information across multiple images to capture common structures.
The main contributions of this paper are summarized follows:

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We identify the weakness of previous similar representations and propose a refined rep- resentation, Factorized Features, based on thorough analysis as in section [.1 for coarse and fine details of images via explicitly modeling multi-scale visual features and structural components.
We generalize such image descriptors to learned settings super-resolution and image compression, with potential applicability to broader low-level vision tasks.
We demonstrate hate-of-theeart performance on benchmarks for both super-resolution and image compression through extensive experiments.
Related Works
Huper-RResluttin (SR). Image super-resolution (SISR) aims to reconstruct high-resolution (HR) images from low-resolution (LR) inputs, which is crucial for computer vision. Early CNN-based methods (4 59
113
89
43
introduced residual 48
61 94 112
21 58 and recursive learn-
ing [19 90]. GAN- based approaches [47 [48 97 98 improved perceptual quality but faced spatial-
locality constraints. leading to Transformer-baseee based SISR models [14 [3). SwinIR (55) integrated window attention with Swin Transformer [69], inspiring further advancements [22] [19, (1]. Hybrid models such CRAFT [50]. DAT [88. and HAT [15] optimize feature aggregation, while RGT 19 enhances spatial details efficiently. Recent efficient Transformer variants such Restormer [105] and Uformer [99] demonstrate that lightweight attention or activation-fres frree blocks can match or surpass heavier designs. Diffusion-base
[09
methods such as DDRM 42 provide an
orthogonal line of plug-and-play restoration priors, with recent advances extending to video restora- tion [104) reference-based face restoration (37]. and inpainting tasks (64). Additionally, learned pipeline approaches (68 reverse the image formation process for reconstruction tasks.
Spectral Coordinate Transforms. separate line of work seeks to encode coordinates rather than deepen the backbone. Fourier Features [91 78) map input positions to fixed harmonic basis, enabling MLPs to model high-frequene detail. CoordConv [65] expands convolutional layers with raw (ar, y) channels facilitate spatial reasoning. On the other hand, sawtooth coordinate transformation (-), of our Factorized Features, folds space into piece-wise linear triangle wave and produces evenly spaced spectral peaks (see section (41) that favor sparse and low-rank Factorized Features. Unlike the above encoding, our basis-coefficient decomposition paired with ? can be trained end-to-end and reused directly in both super-resolution and compression pipelines.
Image Compression (IC). Deep learning surpasses traditional codecs such as JPEG
and
JPEG-2000 1921, with based 8 4 33), Transformer-basel [45] [15 100 25
27 106 67
229, and GAN-based [73] 74 26 86 approaches improving performance. ELIC [3] introduced
adaptive coding; LIC TCM 62 combines CNNs and Transformers; eContextformer 46 leverages
spatial-channel attention. Grouped.Mixer [51] introduces token mixers, while Wavelet Conditional 88 balances perceptual quality and distortion. Generative codecs such HiFiC [77]
Diffusion
pursue high-fidelity reconstructions at extremely low bitrates and offer a complementary direction to likelihood-based models.
Our work diverges from these trends by introducing Factorized Features, a unified framework modeling both visual and structural features to enhance performance across super-resolution and image compression.
Frequency Decomposition Preliminary
In this section, we start by revisiting several previous renowned representations for images, e.g., 2D Fourier Transform, Learnable Fourier Series [66], and Factor Fields [12. and then generalize them to concise formulation of basis-coefficient decomposition in eq.
The Fourier Transform has long been used in many scenarios to represent periodic or finite signals with a group of sinusoidal functions. In practice, it often takes the form of the Discrete Cosine Transform for a real-valued 2D discrete signal with height // and width W:
f(
Σ
Σ and
Su.v cos
mu
x + 1
cos
TV W
+
1 2
(I)
H
U
where Su, is the amplitude.
3

---

Without the loss of generality, we consider square images in this work, with edge length (and also the period) denoted as T':
M1. = EE Su, cos
2TT
[ur + vy) - Euze
(2)
T
where x < T, 7, and Eu, phase shift.
In image processing tasks, the goal is to learn S and E, then use the formula above to reconstruct high-quality images from degraded inputs. To achieve this, [66] treats S and & as learnable parameters, allowing the model to optimize them for better reconstruction. Furthermore, the frequencies u and are also designed to be promptable by the model, enabling dynamic adaptation to spatial-varying high- and low-frequency components.
More generally, can formulate it as the multiplication of coefficient and basis b with simplified notation, and in this work, we use x to represent the pixel coordinates (ar, y):
N
f(x) Σ b,(x), bx(x)) = cos [[u, + m.)) -i):
(3)
where N denotes the number of frequency components.
In the next section, starting from the concise formulation in eq. 3 we introduce our Factorized Features framework and elaborate its spatially variant coefficients and adaptive basis functions, while showing its application to super-resolution and image compression.
4 Methods
In this section, we dive into the motivation and how we resolve the weaknesses of previous decomposition- methods by our Factorized Features in section 4.1 Next, we discuss how to integrate such strategy into learned settings of Super- Resolutinn in section 4.2 and Image Com-
pression section 4.3 We provide the background of learned image compression in the supplementary materials.
4.1 Formulation of Factorized Features
In this subsection, we focus on the analysis of the properties from different factorization components, and derive our final Factorized Features through these insights, starting from the simplest expression eq. (3)
Spatially Variant Coefficient. Intuitively, the local frequency spectrum of a signal is spatially variant, meaning that different regions exhibit distinct spectral characteristics, c.g., certain regions of an image do not require be pptial-varying following [12], i.e.,
components. Therefore, in this work, we set coefficient oj to
f(x) Σ (x) (x).
(4)
Learned Non-uniform Basis. Previous works (66, 54 49 learn basis through frequencies u, v and phase shift &; however, constructing signals with definitive sets of uniform sinusoidal harmonic functions does not facilitate the utmost details. The predefined nature of these sinusoidal functions re- stricts local flexibility, making fine-grained adjustments more challenging. Also, since low-frequency components typically require more energy (52), during the learning process with training losses of MAE MSE, models would attend more to low-frequency parts and sacrifice local details, As shown in fig. 2a] higher frequency components converge after their counterpart. Hence, in this work, we generate the entire basis map b; M, HT'x for better fitting and local reconstruction.
To this end, we have introduced our rough idea: Under the generalizable setting, we use networks to generate multi channel coefficient map and multi-channel basis map, and combine them. In this work, the composition process happens in the end with projection function P for RGB images î:
f(x) = P Concaat 1=1 { (x()) (x())) -x()))) }})
(5)

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High Frequency
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(a) (x) = cos [uu. v.y) Ed] (b) bx(x) cos [1,,3 + v.y) E.] (c) b. cos (on M.) + cos (.2
Figure 2: Comparison of different trainable basis settings We test on single-image regression with f(x) Eis (x(x) (x) with equal parameter count. (a) fixed sinusoidal basis favoring
frequeeyyy content, eq. (3); (b) learnable (i.e. requires gradient) coordinate mapping with moderate gains; (c) Learned Non-uniform Basis M, RT'T converges more synchronously. Note that 1 02 are the frequencies, functionally similar to U, V.
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Figure 3: Visualization of different factorization methods This figure shows the difference between vanilla fields, coordinate transformation, and multi-frequency modulation. Specifically, (a) is vanilla hasis-coefficient field, and (b) adds sawtooth transformation. We can in (b) that the coordinate transformation explicitly models a patch-like pattern, e.g., the second plot from the top is divided into two periods. By enforcing such frequency components, the models can decompose the signal effectively. Next, (d) is our full formulation, while (c) has no a. Intuitively, from (b) to (c), applying s (we use cos here) should not have much effect on the performance since we do have any constraint on these learnable bases. With the introduction of a, the models are forced to attend to signal components of different frequencies.
In contrast previous works which employ Fourier bottlenecks/66), or frequency decomposition among model blocks, here we seek to address fundamental question: Can well-learned representation effectively replace the simple feature map output? That is, our solution is meant to be applied directly on networks to represent any images.
blocks [54 49 52
Next, discuss more improvements on frequency decomposition model image details.
Coordinate Transformation. The success of the Fourier-based representation originates from its sinusoidal decomposition. By using such periodic functions, one effectively analyze and
5

---

(+)
(((()))
ex(e)
ba(tiasz)))
ox(a)
8
9
12
V(as (b)
-afor -ba)
Figure 4: The Proposed Factorized Features. In this figure a (1, 16 = sin(.), and that (x))) coordinate transformation. We can see in this figure with sawtooth transformation y the feature is prompted to learn pattern from different scale in patch-like manner, e.g. 72 makes the same basis repeat four times the grid. However, only 7 is not enough for very fine details; therefore, introduce and v. Each basis is forced to accommodate both high-frequency (large ) and low-frequency (small a:) components together with periodic functions b, i.e., larger a will make ei oscillate sharper. With explicit formulation of repetitive patterns and high frequency components, images can be represented with fine-grained details, which especially useful for low-level vision tasks such Super-Resole
and Image Compression.
reconstruct signals with the enforcement of high- and low-frequency components. However, the formulation eq. (5) does not have such explicit harmonic feature (coefficient and basis are learned maps), and thus in fig. 3 (a) (b)) witness performance loss due to lack of such guidance.
Inspired by position encoding [78 11 81 7 9 and Fourier feature mapping [91]. we introduce
coordinate transformation function 7/8 on before sampling basis by:
f(x) P (Concat (c(e)))((x())))]] (((x())))
(6)
In practice, we empirically [12 use sawtooth transformation (x) mod k, R; visualization is also provided the supplementary material. We argue that the function explicitly imposes patch-like periodic constraints and, therefore, enforces models to learn such repetitive patterns.
Multi-frequency Modulation. 885 has shown that neural networks are biased towards learning low-frequency content. Hence, propose multi-frequency modulation to compel the model to fit high-frequency components, visualized in fig. 3P and fig. 31:
{(>) P (C (Concat-=1y-) 1y=1 ct (x) @ May (((()))))
(7)
where & E sin, cos and a E R. In this way, each basis 6, contributes to both high- and low-frequency components by different values of a. Consequently, if basis is only accurate in the cow-frequency domain, the output will contain undesired high-freug sreh-freyeency noise.
Alternatively, eq. can be interpreted as making the spatial coordinates x, y of bx(x)
cos [u,æ + v.y) E. in eq. B3) learnable instead of the frequency components u, v. To validate this. we conduct experiments (fig- 2b) showing that learning coordinates mitigates the rigid constraint of uniform distribution, aligning better with the non-uniform nature visual patterns across spatial layouts; that is, some pixels share similar RGB values, indicating smooth color transitions, while others exhibit abrupt changes, suggesting high-frequene variations.
To this end, our full Factorized Features representation is formulated in eq. visualized in fig.
4.2
with Factorized Features
We represent super-resolved image using our Factorized Features, where coefficients and basis are generated by networks Frvelt and Fousis from a low-resolution Image:
isR(x) =P (Connatt=1
(x) U(aj 6. (x(x)))))
(8)
where (z)) = F Fewett ( T1R) (x) and (LR = Fhacis (F (Feeer( (I.)) (x)))). Note that we sample the outputs Fowem( TLR) and Frasis (Feeer (IR)) with coordinates and 7<x) respectively. We omit convolution layers here for simiplicity.

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Single image Super-Rroslution
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(b) Learned Image Compression with Factorized Features
Bus Detn
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Compersion
Porkorted Recosioration
Decompressio
Quarriztion
Comprasan
Coalt
Figure 5: Super- Resolueeso and Image Compression with Factorized Features. This figure illustrates how Factorized Features are used Super-Resolution and Image Compression. (a) Given low-rcsolution imput image, first extract x feature with Coefficient Backbone. Next, generate the basis and coefficient with Basis Swin Transformer and convolution layers, respectively, from the same ff Finally, the prediction is reconstructed by Factorized Features Reconstruction. (b) To decrease distortion image compression, we replace the synthesis transform of the traditional learned image compression pipeline with (a) by aligning spatial resolution and latent channels.
Our model comprises three main components: Coefficient Backbone F Feueff- Basis Swin Transformer Fissis, and Factorized Features Reconstruction. As shown in fig. 5a, the process begins with IL E R XxW The Coefficient Backbone extracts features Xeveir E HcCxH which are then used generate coefficients through convolution and pixel shuffle operations. Also, X is fed into the Basis Swin Transformer to produce a multi-scale basis b = {b) (b,,,.,,nl] by E RCo x Me, WW. The coefficients and basis combined to reconstruct ISR R3xelxxWW using eq. (8). where is the scale factor.
We optimize model parameters using L1 loss. To be more clear, when the Basis Swin Transformer is optimized, the basis is optimized simultancously, i.c. the models are trained to adapt to a content- aware basis, not calculated by heuristic rules. This design enables content-aware basis generation: smooth regions get low- wwwffreqeeccy bases while textured areas receive high-frequency ones.
To demonstrate the effectiveness of our method, we use existing SR methods [16] 18 109 as
the Coefficient Backbone. For the Basis Swin Transformer, we employ simple Swin Transformer Blocks 770 with a series of special downsampling operations. Specifically, we use dilation-like downsampling technique to accommodate the 7 sawtooth sampling pattern, where the details and visualization can be found in Supplementary Materials. The final basis is refined using additional upsampling and convolution layers.
4.3 Image Compression with Factorized Features
Image compression balances bit-rate and visual fidelity. Recent work recovers hidden details mainly via architectural tweaks twaak--nnllysis transforms and entropy models [46] [5]] or sophisticated de-
coders 88 25). We instead target the representation itself: our Factorized Features formulation
(eq.
explicitly models structural correlations, boosting quality.
Priors from SR. In addition, with our trained SR model described in section 4.2 intuitively serves as a strong prior for information recovery, i.c., it contains extensive knowledge of how to reconstruct missing details and enhance image quality by leveraging learned patterns from the training data. Thus, since Super-Resolute enhancing image details from low-quality sources, we can effectively integrate this prior into the compression pipeline.
and Image Compression share the core principle of reconstructing and
The overall pipeline is shown in fig. 5p. To demonstrate the robustness of our representation and the effectiveness of the SR prior, the compression and decompression networks greatly follow [62], with only the synthesis transform replaced by our SR pipeline, where the details can be referenced in the Supplementary Materials. practice, the training is performed two stages. After we obtain
trained SR prior, the model is fine-tuned with lower learning rate alongside the compression module,
7

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Table 1: Quantitative comparisons 4x super-resolution with state-of-the-art methods. The best results are colored red. The models with fare those who use the same-task task pretraining [16], i.e., pretrained on ImageNet. Please refer to quantitative results in section 5.1 for details.
Paruns MNCS
Focward Pass
Sec5
Sctl4
Urbun100
MangalU9
Mahhod
(M)
(C)
Menury (MB)
PSNRT
SSIMT
PSNR
SSIMT
PSKRT
SSIMT
PSNRT
SSIMT
PSNRT
SSIMT
EDSR [3% CVVPR117)
43,09
207.07
1,182
32:46
0.8068
28.90
0.7886
27.71
0.7420
26.54
13,0033
31.02
0.9148
RCAN [111 [ECCV 18)
15.59
65.52
1,176
52.65
0.9002
28.57
0.7889
27.77
0.7436
26.82
0.8087
31:22
0.113
SwinlR
63 (1)V 21)
25.01
119.68
3,826
32.93
0.9043
29.15
0.7958
27:95
0,7484
27.56
0,8273
32.22
0.9233
CAT-A-
1x] NIPS Spollight)
16.60
70.20
3,508
33.14
0.9059
29.23
0.7968
26.01
0.2516
27.99
0.835
12.52
0.9233
AKT
[0S ICLR Spoolighh
16.56
69.94
3,010
33.04
0.968
29.16
0.7958
27.97
0,2510
0,8321
32.31
0.285
(VVR)224
20.26
17.10
29.25
0.7524
32.65
09338
(1CCV223)
14.80
0.2518
12.67
RCTT
13:37
834.55
3,404
33.16
0.9065
0.7979
25.03
0.7530
28.09
0.838
32.68
09363
PFT 211
CVVM
19.66
50.21
6,414
33,15
0.9065
29.29
0.7978
28.02
0.7527
28.20
0,8412
32.65
0.936
HAT
13 (3)
20.77
56.02
3,092
33,18
0.9073
29.38
0.5001
26.05
0.7534
25.57
0,5447
32.87
0.9319
ATD L!
69.42
154.3
15,582
33.15
0,9062
29.31
0.7985
26.02
0.7514
28.25
0,8422
32.78
0.9329
ATD-F (Oun)
149.87
26.05
33:11
DAT4 1
43.01
175.22
11,326
0.9084
0.50009
0.2548
33.02
09321
DAT (Ouns
40.00
134.42
6,206
33.45
0,9094
20. 00.60
0.5139
28.15
0.7560
28.75
0,8520
33.23
09339
HAT-L
40.84
167.27
6,804
33.30
0.9083
29.47
0.5015
25.07 09
0,7551
28.00
0.8499
33,09
0.9355
HAT-F (Ouxs)
45,97
158.79
5,750
33,53
0.9180
29.65
0.3050
26.15 18
0.7569
28.70
0.8527
33.33
0.532
HAT-L-3" (Qun)
66.14
240.03
8,888
33,75
0.9116
29.87
0.3091
26.31
0.7997
29.51
0.8657
33.36
03933
HAT-I-RavisFinn (Our, ablation)
46.67
161.66
5,696
33.33
0,9085
29.47
0.9015
28.10 10
0.2584
28.57
0.5494
3311
09336
IAA---Coocaa (Ouns, shiution)
45.52
129.05
0,9095
29.57
0.2566
0,8518
33.28
which is then trained end-to-end with common loss function used in learned image compression, defined as
L = R(O) R(2) À D(x, 2),
where 8 is the hyperprior, R(-) refers to the bit-rate cost, D(-) is the distortion term, and À controls the trade-off.
4.3.1 Multi-Image Compression
Intuitively, different images often share common frequency components. By learning single, shared set of basis functions, we can leverage the frequently appearing similar or repetitive patterns across images to greatly reduce coding redundancy in multi-image compression. In practice, this means fewer total parameters and lower computational cost required when compressing an image collection.
Each per-image basis by E Cs, xHs, x Wb, captures local pixel structure. We fuse the M bases into a denoised, generic basis with a transformer Fmerge 83 applied at every position:
b, (h, w) = Fimerge ((b (h, w) I E L))..
(10)
Treating bases tokens (prepended with CLS token), the transformer's output forms the merged basis.
Because compression noise corrupts the coefficient map X (fig. 5p), feeding it directly into the Basis Swin Transformer would amplify errors. Instead, we transmit the merged basis separately, alongside the quantized variables Q 11), 2, and reconstruct each image with this clean basis plus its own decoded coefficients, yielding higher quality at similar bit-rates. A single- vs. multi-image compression comparison is in the supplementary materials.
Experiments
In this section, we provide the experiment setup and performance of Super-Resolution and Image Compression tasks. Please refer to Supplementary Materials for more ablation studies, training, implementation details, and analysis.
5.1 Image Super-Resolution
Experimental Setup. Following the same-task pretraining strategy of [5| 21 Resolution (SR) models on Ima3eNet(33). Our Factorized Features plug shared Basis Transformer into four pretrained SR backbones-Swe (55), HAT (16), DAT [18] and ATD [110]. Backbones
we pretrain all Super-
8

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HR
Bicubic
BSRGAN
SwinIR
Full Image
ESRGAN
RGT
DAT
FIPER (Ouss)
HR
Bicubic
BSRGAN
SwinIR
Full Image
ESRGAN
RGT
DAT
FIPER (Ours)
Figure 6: Visual comparisons on super-resolution (4x). The proposed method achieves the best reconstruction results compared the reference HR images.
keep their original weights, while Basis Transformers start randomly. Pretraining runs 300k iterations on ImageNet with Adam (Ir 2e-4, batch 32, 3 0.9/0.99); finetuning runs 200k iterations on DF2K (DIV2K [[]liikrr2K (59) with Ir le-5. Inputs are 256 256 crops, bicubically down-sampled to 64 x 64 for the backbone. We set the number of coefficient-basis pairs to N = and use frequency scalars Og (1,4, 16, 64) capture both low- and high-frequency details.
Quantitative Results. presentts the quantitative comparison between our approach and state-of- the-art (SoTA) methods. We evaluate the methods using five benchmark datasets, including Set5 (6], Set14 [17]. BSD 100 [75). Urban100 [38], and Mangal00 109 (76). For quantitative metrics, PSNR and SSIM reported. Our model delivers 204.4% average PSNR gain, defined as (c- b) b) with b=SwinIR, a=HAT-L, and c-HAT-L-F. We embed three SoTA SR backbones: ATD [109). DAT (18] HAT [16], yielding ATD-F, DAT-F, and HAT-F Each beats its parameter- parameter-matched baseline (ATD-L, DAT-L, HAT-L). As only HAT provides large variant, we upscale ATD and DAT to the same size and train all models with identical pre-training and fine-tuning for fairness.
The Order of Coefficient and Basis. Furthermore, in traditional Fourier Series and other image processing methods 195], the basis is typically derived first and then used to compute the coefficients. In contrast, our method derives the coefficient features first, as illustrated fig. 55. To explore this difference, develop another variant of our model, denoted HAT---Basis-Fiig the order of operations. then the resulting basis features and the image input derive the coefficients. This approach, however, leads to a gigantic performance drop, showing the importance of the order of the pipeline. Specifically, argue that in our pipeline, the Coefficient Backbone functions more feature extraction module, where the refined features facilitate downstream basis extraction.
where reverse this case, we first pass the image through the Basis Swin Transformer and
The Importance of Factorized Features Reconstruction. Lastly, to evaluate the effectiveness of our Factorized Features, we trained model named HAT-F-Concal, which does not apply the formulation in eq. (7). Instead, it concatenates the basis and coefficient directly and decodes the resulting features to produce the output. Although this approach results in reduced performance, the Basis Swin Transformer with Sawtooth downsampling still contributes to improved reconstruction, even without Factorized Features Reconstruction, highlighting its effectiveness.
Visual Comparison. We provide the visual comparison in fig. 6 The images are randomly sampled from the DIV2K dataset. Our method faithfully reconstructs the image details, whereas the other approaches suffer from over-smoothing hallucinating details absent in the ground truth.
5.2 Single- and Multi- Multi-Image Compressions
Experimental Setup. Image-compression experiments follow the SR protocol (section 5.1). Mod- els pretrained on ImageNet and fine-tuned for 200k steps 256 256 crops. Compres-

---

38
36
38
PSHA (d8)
PSHA (48)
Des loverd
Tha peeccal
34
32
Fand
pand
28
30
0.6
0.4
0.9
1.0
Bit-Rate (bpp)
Bit-Rate (bpp)
Bit-Rate (bpp)
(a) Kodak
(b) CLIC
(c) Tecnick
Figure 7: Performance (RD-Curve) evaluation on image compression using different datasets.
Table 2: Comprehensive evaluation for image compression. Using VTM as an anchor for calculat- ing BD-Rate. Latencies are measured under an NVIDIA GTX 3090 GPU.
Method
BD-Rate (%)
Total Encoding Time ())
Total Decoding Time
Params(M)
VTM
0.00
129.21
0.14
Cheng 20)
Xie (I
-0.78
2.93
6.00
50.0
STF (CVP) 116
-4.31
0.14
0.13
99.9
ELIC [2)
-7.24
0.07
0.09
36.9
TCM (CVPR'33)
0.16
SegPIC (ECCV"24)
[67
-8.26
0.14
0.13
83.5
LALIC (CVPR'25)
27
-15.26
0.27
0.15
63.2
TCM-HAT-L-F (Ours)
-21.09
0.109
0.264
110.34
TCM-HAT-F-mult M=1 (Ours)
27.96
0.2320
0.1742
131.35
TCM-HAT-F-muil M=2 (Ours)
2.70
0.1998
0.1270
131.35
TCM-HAT-F-muli M=4 (Ours)
-10.11
0.1846
0,1039
131.35
TCM-HAT-T-muli M=8 (Ours)
-16.61
0.1756
0.0922
131.35
TCM-HAT-F-multi M=16 (Ours)
-19.88
0.1715
0,0863
131.35
TCM-HAT-F-multi M=24 (Ours)
-20.97
0.1702
0.0844
131.35
sion/decompression networks start from TCM weights 662 and are optimized end-to-end with AdamW (Ir le-5, batch 16, 3 99) [72). Integrating our SR module into TCM yields TCM- HAT-F and TCM-HAT-L-F; TCM-HAT-F-mull: is the multi-image variant.
Rate-Distortion Performance Comparison. We compare our model with State-of ofate-of-theAArr Ahe-Art learned
end-to-end image compression algorithms, including (63] 13,, [116], [ION] (20] B3.
[5]] 440.
5
and [36]. The classical image compression codec, VVC 993 also tested by
using V.M12.11 1.M12.1Thh The rate-distortion performance on various datasets, including Kodak, Tecnick's
old test set with resolution x 1200, and CLIC Professional Validation, is shown fig. TCM- HAT-L-F achieves a -21.09% BD-Rate vs. VTM (Table 2), surpassing earlier work. Multi-image mode (TCM-HATT-F-muttt scales well, reaching 20.97% at M sending a shared basis curbs Coefficient-to-Ban error, though distortion grows slightly basis capacity is stretched. Across Kodak, CLIC, and Tecnick, FIPER consistently boosts rate-distortion and maintains competitive latency.
6 Conclusion
We proposed Factorized Features, a representation that decomposes images into multi- freeuuneyynyyy components to model implicit structures and patterns. Our approach addresses challenges in Super- Resolution and Image Compression by effectively restoring details and preserving visual fidelity. We integrate SR priors with Image Compression for better information recovery and introduce basis-merging technique to enhance multi-image processing performance.
Limitations. Although effective, our method requires further optimization for ceapputatioo-lmmiitee scenarios such as real-time decoding. Additionally, incorporating semantic information remains promising direction for future research.
10

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Acknowledgements. This research was funded by the National Science and Technology Council, Taiwan, under Grants NSTC under Grant AS- CDA-110-M09, and Yin Shu-Tien Foundation Taipei Veterans General Hospital- National Yang Ming Chiao Tung University Excellent Physician Scientists Cultivation Program, 1 114-Y-B-144. The authors are grateful to Google, NVIDIA, and MediaTTek Inc. for their generous donations, and we would also like to express our sincere gratitude to fia-Wei Liao for valuable assistance in paper writing and revision. Yu-Lun Liu acknowledges the Yushan Young Fellow Program by the MOE in Taiwan.
--902---44000-MMYY-
113-2628-E-A49
Academia Sinica
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A Overview
This supplementary material provides additional implementation details and experimental results to complement main manuseript. Our FIPER framework explicity models multi-scale patterns and captures periodic features effectively, as visualized in fig.
nAT
BSD100 x4 img_096 236_SRF_4
FIFER
Figure 8: Visual comparisons on super-resolution (4x).
In the following, we dive into the details. Specifically, we first elaborate on coordinate transformation, the background of learned image compression, and comparison between single- and multi-image compression in appendix [ which were omitted in the main paper due to space limitations. Following this, we discuss the differences with factor fields [12] in appendix C Next, appendix [D] we present comprehensive details about the experiments and benchmarks, including the Video Super-Resolution task, which was not discussed the main paper. Then, we provide ablation studies regarding different components of our pipeline, validating the design in appendix B Finally, provide extensive visualizations to facilitate a more detailed comparison of the results in appendix H
B Method Details
In this section, we provide the details of Sawtooth coordinate transformation and downsampling inspired by it, the background of Learned Image Compression, and comparison between single- and multi-image compression.
B.1 Sawtooth Coordinate Transformation and Downsampling
Sawtooth transformation Sawtooth transformation is formulated as 7(x) x mod k. k E Re can easily observe that such transformation implicitly captures patch-like frequency information as shown in fig. 49. and thus, we propose that by leveraging the inter-patch information from the sawtooth coordinate transformation, the visual correspondence between spatial locations can be effectively represented.
Downsampling based Sawtooth transformation To reconstruct 256 x 256 image, formulate our Factorized Features as
[(x) = >P(Concat N K
((=))>(Coom))) (
{ ( (zy(x)
vlay b((((=))))
(11)
which is the same eq. 7 in the main paper.
In practice, the bases are of shape
W with = We set (256, 128, 64, 32, 16, 8} and C 24 for all bases. Thus, sample each basis with (z)
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Transformed Coordinate sample
Roumange
Transfomed Cooriinste
(b) Pixel Unshuffle
sample on
Sample
Reenwagg
(a) Sawtooth Pixel Sampling
(c) Sawtooth-Awan Downsample
Figure 9: The correlation between coordinate transformation and downsampling. (a) The sawtooth transformation example with k 2. (b) The PixelUnShuffle downsample. (c) To ex- plicitly model the information for sampling with a sawtooth, we rearrange the feature map in dilation-like manner in the downsample layer of the Basis Swin Transformer. This way, the feature sampled would capture the information in the original layout correctly; in other words,
I Sawtooth-Pixel Pixel-Sampling Suwtoothh-Awarr-Dowwsss
mod K; where x E {O..... 255]² and {256, 128, 64, 32, 16, 8). This formulation can be in- terpreted sample the same feature different spatial location of image, e.g., when using b1 22241288122 with b 128, x = {0, 0} and = {128, 0} will be extracting 6 0), which is also visualized in fig. h. Therefore, we want to aggregate the information appearing in different location of the image, where these spatial locations will be sampled at the same location on the basis; that is, want the information of [(0, 0) and [(128, 0) be aggregated in bı (0, 0) in previous example. This way, we can explicitly model repetitve structure in different scale, and such frequency modeling subsequently enhances the reconstruction.
Based on the analysis, as visualized in fig- D.. we integrate Sawtooth-Awan Downsample layer into Basis Transformer. Such operation is essentially the inverse of Sawtooth transformation, i.c., merge the feature together with Sawtooth- -wwrrr Downsample, decode the feature to basis, and then sample the basis to different spatial location via Sawtooth transformation.
B.2 Learned Image Compression.
Following
learned image compression model with channel-wise entropy model can be 79 formulated as:
ha db), ga (x; o),
{ Fmean, F Fsate h2(2; 0n), = Q(z),
(12)
D (Q(yo - po) + Na, Q - me) + me) (T: 0), 7 Refinee, (Ho, .... Mr, D),
where 0 <= t t PL cs(ici F. The encoder Ia transforms the raw image into latent representation y. hyper-prior encoder he further processes y to output 2, capturing spatial dependencies. 2 is then quantized to E, where factorized density model is used to encode quantized as ( yp = II, (pp)))())))))))))))){())))) l (-2, 2)) (žz) where j specifies the position or each element of each signal. The derivation the equation can be found in (2]. Next, decoded by h, to produce features Fmean and Fscale, used to estimate the mean μ and variance of y. The latent y is divided into / slices, and each quantized around computed means μ4: These μ4 are derived from earlier quantized slices and Fmean by slice network decompression, ý is refined using Refines, based on 14, and ý to produce y, approximating the original Finally, Ss reconstructs the decompressed image à from J. The model is trained using
The quantized slices form ÿ. For
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Lagrangian multiplier- based rate- distortioo optimization:
+ R(2) X (zz .) L +
[- loga (Po)= (9 2))] E [- log2 (Pa (8) [))]
(13)
A D (x,
where R(U) and R(2) denote bit rates, (xx, .)) is the distortion term (calculated by MSE), and X balances compression efficiency and image fidelity. our experiments, we follow [62 modifying only ys to demonstrate our representation' effectiveness.
B.3
Comparison between single- and multi-image compression
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Figure 10: The illustration of our image-compression framework (a) Traditional learning- based compression methods. (b) Our approach surpasses (a) by incorporating our Factorized Features and Super-Resolution (SR) Module from section 4.2 in the main paper information-recovery prior. (c) Expanding on (b), we introduces a multi-image compression strategy that utilizes both our SR Module and Basis Merging Transformer capture shared structure.
We provide visual comparison of single- and multi-image compression in fig. 10p and fig. T0p, respec- tively, with traditional compression method in fig. [Oa. First, we have single image compression(SIC), the same as fig. 5b in the main paper. The goal of the SIC pipeline is to validate two aspects: (1) that Factorized Features, which are designed represent images, can be applied different tasks; (2) that leveraging super-resolution (SR) priors improves reconstruction quality, Note that we directly adopt the SR module's 's architecture to also reduce overall complexity.
Next, we derive multi-image compression (MIC) as in section 4.3. of the main paper. In traditional signal processing, shared set of bases often used represent diverse sources. We adopt this property to further reduce compression redundancy. Specifically, our approach transmits (1) image features, which are used to decode coefficients, and (2) the bases themselves. By contrast, single image compression in fig. [Öp transmits only image features. Intuitively, transmitting the bases provides additional information that can improve reconstruction quality. However, directly transmitting all bases would significantly increase the bit rate. To address this, we merge the bases into a single set before transmission, thereby enhancing reconstruction while minimizing extra transmission costs.
C Differences from Factor Fields
We explicitly highlight how Sawtooth-based sampling and Multi-frequency Modulation extend the original factor fields. In 2D toy examples shown fig. [1] traditional SR/IC representations can be viewed as a "vanilla" scenario with N = and c(z) 1. factor fields already improve accuracy over such baselines, but our introduction of and a further captures both high- and low-frequency details. Specifically, forcing = 4 compels the network to learn broader frequency ranges and avoid noise from the fixed modulation. To confirm these advantages, we trained smaller SR models and compared them with factor fields in table The results illustrate that multi-frequenn constraint
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yields significant gains even in simpler configurations, underscoring its importance for high -reufffreeeney detail preservation and overall reconstruction quality.
()) Convergence curve
(b) Target image
(c) Vanilla fields
(d) Factor fields
(e) Ours with y only (f) Ours with and
Figure 11: 2D toy example.
Table 3: Comparison with Factor Fields. HAT-FA-Small denotes replace our Factorized Features with factor fields.
Methad
Saorsooth n(e)
Param:
MACS
Fresont Paes
Ser5
Setl
Lifoan 100
Monga 109
[M)
Menror (MB)
PSNX
SSIMI
PSNRR
SRIMI
SSIMI
PSNK
SSIM1
PSNR1
SSIM1
HATS
3,214
32.52
0.9047
29:15
12.35
0.9283
HAY
30.77
1,690
13.04
0.9194
18.25
0.2973
38.00
0:3517
17.97
0.3168
12.48
0:9291
HAR-RA-Small
15.00
57.81
1,678
13.06
0.8263
18.25
0.7906
36.04
0.7534
78.12
0.8411
12.53
0.930
HST Small sin
[sin]
11,4,36.00
16.13
06.34
4.176
33.16
0.906
29:33
0.7989
28.05
0.7500
28.36
03423
12.64
0:3312
ons
(1.18)
16.13
0.9073
Small
10,04)
HATE (Oer FTPF3R)
(1.4, 16,01))
45.99
158.19
5,790
11.
0.938
19.55
0.8011
18,09
0.588
18.55
03463
12.99
0.3199
HAUL (InageNee sainsd)
40.4
167.27
6,804
33,30
0.983
29.47
0/0115
28.09
0.7551
28.00
0:408
33,09
0,9335
D Implementation Details
The architecture our SR networks is shown fig. 12 Firstly, for Coefficient Backbones from various pre-trained models like [15 109 18] we replace the output upsampling layer (mostly pixel shuffle) with convolution channel D 256, i.e., for input image with resolution 64 x 64, the original pre-trained models process hidden states in 64 64, and then upsample the output to 256 x 256 for final result, where we replace the upsampling with convolution and output the final hidden state Xcoeff E 2456664x64
Single Image Super-Resolution
Next, the Basis Swin Transformer begins with feature embedding, extending the channels D from 256 to 384, where the features are then passed through series of (70 and Sawtooth-Aware Downsampling Blocks. Specifically, each block contains two layers, one of which uses shifted window attention. After each block, the hidden state goes through upsampling by 4x and convolution to convert the output basis channel to 24. Then, Sawtooth-Awan Downsample block rearranges the hidden state h as discussed in the main paper, which can be viewed as:
= rearrange(I, h, c (s h) (s w) + c c) w'), 8 ==
(14)
and reduces the feature channel by 4. In all experiments use N 6, i.e. there are 6 bases, where Basis; E 24 259 x 256
2
for in ..... ...5) 5}.
Finally, we derive our Coefficient by series of Convolution and Pixelshuffle layers and decoded the Bases and Coefficient predicted high- high-resolution image by eq. (15):
i(x) P (Cooncat N
(z) @ (ay b((()))))
(15)
In practice, the coefficient is generated with channels equal to the total number of base channels, and it is split accordingly by channels.
Multi-Image (Video) Super- Resolutin Building upon our prior work in Single-Image Super- Resolution (SISR), we extend the applicability of Factorized Features to tackle the challenges in Multi- Image Resolutio (MISR). In the main paper, introduced the Basis Merging Transformer for Image Compression. Here, we further expand its functionality to generate per-timestamp Coefficients and Bases.
To evaluate the effectiveness of our approach, we use Video Super-Resolution (VSR) as the benchmark task. Specifically, we simply leverage transformer blocks from [8 to model temporal correlations.
28

---

Embodiing
Swind Block
Platthuflee
ILA Rasltww
Comv
Basis
Bewlooth-Aware Downsample
Xoet!
X.N
Pustihute
Cotv
Con
Core
Coaficient
Figure 12: Detailed architecture of Super-Resolution Modules
Frames REDS/Vimeo
REDS4
Vimeo-90K-T
Vid4
Method
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
VSR++ 10
30/14
32.39
0.9069
37.79
0.9500
27.79
0.8400
VRT 57
16/7
32.19
0.9006
38.20
0.9530
27.93
0.8425
RVRT 56
30/14
32.75
0.9113
38.12
0.9527
27.99
0.8462
PSRT 87
16/14
32.72
0.9106
38.27
0.9536
28.07
0.8485
IA-RT 102
16/7
32.90
0.9138
38.14
0.9528
28.26
0.8517
Ours -aTT-
16/7
32.67
0.9096
38.09
0.9512
27.95
0.8441
Table 4: Performance comparison among different methods on REDS4, Vimco-90K-T, and Vid4 datasets. Note that don't any special design on the network, such as temporal correspon- dence or motion sampling like previous works, demonstrating our effectiveness.
For given video, we first derive the Coefficient and Basis for each frame and rearrange each level i of the Coefficients Basis such that the spatial dimensions H and W are treated as the batch dimension, while the temporal dimension is processed as a sequence of tokens for the Transformer. Next, we apply positional embedding to the tokens, process the tokens with the transformer blocks, and finally decode the Coefficient and Basis token from the respective position with convolution layers for the output super-resolved frames.
table D shows quantitative comparison with state-of-the-art methods. All VSR experiments were conducted using bieubic 4X downsampling. The training dataset includes the REDS 82) and Vimeo- 90K 103 datasets, while the testing dataset comprices REDS4 Vid4 60) and Vimeo-90K- T[003]
For the REDS dataset, we train for 300k iterations using 16 input frames, with a learning rate of le-4 and cosine learning rate that gradually decays to le-7. The batch size is set to 8, and the Coefficient Backbone and the Basis Swin Transformer are initialized from SISR. When training on the Vimeo-90K dataset, first conduct 300k iterations with 14 input frames with flip sequence, we then train model on imput frames with flip sequence, using a learning rate of le-4 and a cosine learning decay 1e-7. We initialize the weights using the model trained the REDS dataset. The batch size remains 8. Note that the training is only conducted on the newly added transformer blocks, i.e., the Coefficient Backbone and Basis Swin Transformer REDS model are reported on the REDS4 dataset, while test results for the Vimeo-90K model are reported on Vimeo-90K-T and Vid4, We calculate PSNR and SSIM on the RGB channel for REDS4 and Y channel for Vimeo-90K-T and Vid4, following previous work 102 87 (6).
frozen. Test results for the
Single Image Compression discussed in the main paper, to make a fair comparison with the sate--of-the-at. entropy model and compression backbone greatly follow that of (62), as shown

---

Recade RC
Ammon E R R (H,
TOM Block with upsample xQ
Our SR Module
& R
imoom
enc
dec
9
Conv
Slice Network
TCM Block with upsample xL
TCM Block with upsample xL
Dasule
TOM Block with downsample xL
TOM Block with downsample xK
E RCxxH,xW;
y HC
E R&=H&W
dec
Figure 13: Detailed architecture of Compression Modules
in fig. 13 more details can be bound in 62 What we do here is that we use the output from the last main layer and convert match the hidden channel of the SR Module.
Multi-Image Compression Following VSR, we use transformer blocks to merge the bases. The difference here that we additionally prepend CLS token that basis, i.c., if we have 16 bases of W = H 64 to merge into one, we rearrange the 64 x 64 tokens as batch dimension, use the 16+16 as sequence dim, and finally treat the additional ICCLS) token as output. For the merged basis compression and transmission, we utilize the same architecture of the image branch, i.e., we randomly initialize a module from 62 with input and out channels change. After the Basis Merging Transformer is trained, we follow the same training setting for Basis compression while randomly sampling images for batch and setting only the Basis compression module trainable.
the final merged
E
Ablation Studies
E.1
Merged-Basis Strategy & SR Priors.
The SR prior accelerates detail recovery by leveraging high-resolution knowledge while basis merging exploits shared structures for efficiency. Since merging is introduced after, the compression model pre-trained, and improvements stem not only from the SR prior but also from the well-initialized basis merging. When trained from scratch (see table the merging transformer tends find a universal solution rather than image-specific structures. Additionally, merging inevitably causes information loss, prompting the coefficient branch to encode more image-specific details. This mutual offset between SR prior and basis merging ultimately strengthens approach.
30

---

SCM--AT-F-muill
TCM-HAT-F M = 24 Coeff-Frozee TCM-HAT- Mmmnti 24 Scratch
BD-rate %
-20.97
-19.18
-18.4
Table 5: Comparison of Merged-Bane Basis Strategies.
E.2
Encoding/Decoding Times.
Fig. 5(c) processes each of the M images through the Coefficient Backbone, Basis Swin Transformer, and Basis Merging Transformer, then compresses and transmits the merged basis. In Tab. 2. different M values primarily affect the run time of the Basis Merging Transformer. Although merging larger M increases computation, per-image overhead remains small once averaged by M, as shown in table o Notably, Tab. 2 assumes each image's basis is compressed independently. which can be confusing. in practice, merged basis is processed only once, so averaged encoding/decoding time is more realistic.
.M
=
M
M
M 16
M 24
Total Basis Merging Time (sec)
0,00328
0.00628
0.01140
0.02312
0.04784
0,08064
Averaged Basis Merging Time (sec) by M
0.003288
0.00314
0.00285
0.00289
0.00299
0,00336
Averaged Merged Basis Compression Time (sec) by M
0.0645
0.0323
0.0161
0.0081
0.0040
0.0027
Decompression Time (sec) by Adjusted Enc Time (sec) by M
Averaged Merged
0.0039
0.2320
0.1998
0.1836
0.1756
0.1715
0.1702
Adjusted Dec Time (soc) by M
0.1740
0.1272
0.1039
0,0922
0,0863
0.0844
BD-Rate %
27.96
2.70
-10.11
-16.61
-19.88
-20.97
Table 6: Comparison of Encoding/Decoding Times.
E.3 Inference Time Comparison for SR.
We provide the inference time in table compared with extensive SR models. The inference time of different components of FIPER is also provided.
ATD
DAT
RGT
HATS HAT HATL, HATRODI Confiction Buckhore (RAT-F) Baik Swis Transtonee (IXT-F) Foctorieed Features Recientracioo (RAT-P)
Inienmen Fire 14) 0,8922
00812 0U087
0.778
01132
0.0134
Table 7: Inference time comparison for SR.
E.4 Influence of SR Priors in Image Compression.
We conduct experiments with various configurations verify our image compression pipeline's effectiveness. TCM-HAT refers to using the original HAT [16) instead of our SR Module in fig. 10pp TCM-HAT-F represents full pipeline, while SCM-HAT-F-Scrallee randomly. Results demonstrate that integrating SR priors improves image compression performance, and our representation further enhances results, highlighting the robustness of Factorized Features.
initializes the SR Module
Table 8: Validation of the effectiveness of SR prior. The best PSNRs are marked in red.
Soubt
Tecck
Metao
(16022
111667
1.m 11.02
EL0023
11.0667
A.m
11.25
3. D19325
5
(1.0077
00221
1pp
1gp
2.2
1Sp
PSNST
1gp
155
PSNRI
197
155
PSNART
10g
TCU CH
133533
10/00/4
0 2583
32 5151
36 1345
01214
$13500
3335
54. 55.990
0.200
12:330
01:N8
33 1755
0.3193
0.5561
36 53.955
BA211
011356
36.1233
TCM
11:567
10.1543
93
2363
$18933
54
04511
373386
54.134
TCM-HATE
01:34
304412
0.398
32 9100
BA276
33.44 6481
01229
33.1917
0.349
34-4009
04812
3733335
011255
134480
01396
34,3066
03915
37.3344
E.5 Effectiveness of Factorized Features Design.
We conduct experiments to verify our multi multi--reequecy modulation. The quantitative performance reported on single-image regression is shown table where each result is measured after 256 iterations. Compared to baseline results, our refinements in modeling pixel-level frequency have significantly improved all performance metrics. Additionally, our results demonstrate that the modulation function zi and the scalar are interdependent, each essential to the other's 's function.
31

---

Table Comparison improvements of Factorized Features, & and a are the same in eq.
(
Note that here we test on single-image regression
Metric
PSNR +
SSIM +
LPIPS +
Baseline 12
22.04
0.505
0.5296
Ours
38.44
0.999
0.0385
No a/ to control magnitude
13.46
0.147
0.766
No a for pixel-wise frequency information
21.25
0.537
0.527
Sed
PSNR/SSIM
Urbant PSNR/SSIM
PENR/SSI
Seanii-a
2229
65.6
520
12,44/0.9776
25.77
25.77/1.7000 200
2G59/2080
26.47 (10)
3112 1131
180
12-43-0.9915
Omei5R
51.9
59
7859
35.115/3055 5.355
00
aRRermenl
387
60.8
$73
13. 51 8185
3550 7577
30331 7333
36,07 5033
31 17/00 9165
XTD-3
1001
12.51-0
7300
77.3922 74400
11
ASTI-D
1931
38.00
57.76 543440
36.29
ManbvlR-F
15.
B16
538
32 07/88/20 7800
16 13.77/0330 7661
33 91 (0971
756
7907
11
RCAN
$2.2
9355
15502
12.53 00.9002
28.57 0.7050
15:31/53336
26.82 (0.5007
31 (0.173
CAZANA (CNR
102.4
40.3
355
22.58/0.9928
25.00 0.750
20/5/50042 50447
25,87 5081
31 009553
CATANN--
110.3
96.7
12.09009001
2389/00
37.8/55244 53341
33.05
11 62/67/003 9014
ESC (Dlin))
28.5
754
953
28.99 23.9/007700
27.85 07.55/5.545
/0815
31 11.75/70 9253
Table 10: Quantitative comparison benchmark datasets for x4 lightweight image super-resolution.
E.6 Light-weight Model Comparison
To demonstrate the effectiveness of method under computation-constren scenarios, integrate our Factorized Features framework to state-of-the-art lightweight super-resolution models and observe consistent improvement shown in table
E.7 Task-Specific Overfitting
To confirm that our Factorized Features are not overfitted to a single task, we further apply the same representation to other low-level vision problems such motion deblurring in table [1] and image dehazing in table 12 without any task-specific modification. The consistent improvements across these tasks demonstrate that our features generalize well and capture transferable visual priors.
MHH Ninkel Dolaadi 9IN DMPR 109N: MEMile
Bepiiii
MASHO-S
Mifteer
Reveno
Rffieec GRLD MERN WAW MEWNeFF
1208
23.7
2449
Table 11: Performance comparison on the GoPro dataset for motion deblurring.
Marric Matkel Delambie
A0D-5a
NSBON
FRA-6
AICB-Na
Delkue:
Ditardiooa::
ToleFarer
LIKN MITM::
PGIENe
Candi (TRAMESH CHnnERLE
51D4
643
641
048
8.45
647
025
031
0.1
5.5
0360
B
6333
Table 12: Performance comparison on the Dense-Haze dataset for image dehazing.
E.8 Analysis of Model Hy Hyperparameters
We further conduct comprehensive study on three key hyperparameters of our model: the number of frequency components N, the frequency modulation a, and the basis transformation y in table [3 and table [4]] These factors collectively control the expressiveness and efficiency of the proposed Factorized Features.
These results show that our design choices provide good trade-off between representation flexi- bility and efficiency, while maintaining stable performance across a wide range of hyperparameter configurations.
32

---

. (Number of Components)
[1.4,
(6.4.16.64)
[1]
{1. 4.16.64)
(1,4, 1024)
32.64
32.69
0L9024
Table 13: Ablation on the number of frequency components N and scaling coefficients We select
N for balanced quality and training efficiency, N 10 yields marginal gains but converges slower.
Set5 Performance /
Sawtooth
Sin
Triangular
PSNR SSIM
32.71
32.69
32.71
0.9027
0.9026
0.9023
Table 14: Comparison of alternative transformation bases
Failure Cases
Failure cases typically involve extremely fine detulls that are absent in the low-resolution (LR) input but appear in the super-resolved (SR) output. However, this has been shared inherent limitation of super-resolution methods to date. For example, in top row of fig. some white structures are prevent HR but completely absent LR.
G Future Generalization
For image generation, for example, can integrate Factorized Features into the VAE decoder of a diffusion model. For video generation, we can employ our mergeable basis and leverage its properties enhance structural coherence.
H More Visualization
H.1 Single Image Super-Resolution
Below, we provide more visual comparisons of single-image super-resolution, where FIPER denotes HAT-F
33

---

DAT
BSD100 X4 img_060 200_0006_550000 SRF_4 44
HAT-L
FIPER (ours)
HR
DAT
Urban100 img070
HAT-L
FIPER (ours)
34

---

Urban100 img046
HAT-L
FIPER (ours)
35

---

H.2 Image Compression
Below, we provide more visual comparisons of image compression. The results are present with TCM-HAT-F and the metrics are PSNR/Bpp.
Original
TCM 32.61/0.3254
PIPER (ours) 33.25/0.3061
C.K. ardrew-n..P-77 376
Original
TCM 46.43/0.0166
HPER (ours) 48.46/0.013.
CLIC 149780
TECKE 1700x1250 dcidbl B01000 son
Original
TCM 38.89/0 1103
FIPER (ours) 40.12/0.1001
Tecrick: www_2200kE200000.OO MALOO0 BO1C0O AGB_cardssa
Original
TCM 10/0.22111
FIPER (ours) 35.93/0.2364
K
K
36

---

TOC Vck. 120LEZ WOODCC D
Original
TCM 34.45/0.2274
RIPER (ours) 35.00/0.2244
To.iddiing Se1ekk,
Original
TCM 41.77/0 0.77
NIFCR (ours) 42 44/0 0415
Tecnick inn 1200G1200 SALUSIL BOIC20 cips
Original
TCM 33.84/0.2900
FIPER (ours) 34.50/0.2766
TWiPt ing 178001700 be nat pmrran araa beghnart
Original
TCM 35 1910
1910
FIPER (ours) 36.06/0 06/0.8418
U
U
M
B
E
37

---

Ternick igg 120.1200022000 3xc.bIR_DO1CO wtt._oooccooooo. roof
Original
TCM 35.52/0.1828
FIPER (ours) 37.02/0 1686
TROTEc Ing
Bañs,
Original
38.25/0.1205
(ours) 38.76/0.112
mng 1200x1300 txt006 701000 AGB pencil
Original
36.61/C.1174
FIPER (ours) 37.16/0 1320
38


Reviews:
[{"review_id": "DccrS0q96V", "reviewer": "Reviewer_yir9", "summary": "This paper is interesting. The authors proposes a 100M network to estimate the best bases and coefficients for feature representation for SR and compression tasks. Experiemental results show obvious improvment in terms of repetitive textures and fine details.", "questions": "Failure cases can be given in the paper.", "limitations": "Can the Factorized Features be overfitted for certain tasks? i.e. task specific.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "A new network design for base and coefficient estimation. \nCan this network be applied to other tasks, such as image /video generations?\n\nStrengths\n1. Unified Representation for Multiple Tasks: Factorized Features generalize across SISR and Image Compression, addressing core challenges (fine detail recovery, structural preservation) with a single framework, unlike task-specific prior methods.\n2. Explicit Frequency and Structural Modeling: By combining basis-coefficient decomposition, spatially variant coefficients, learned non-uniform bases, and multi-frequency modulation, the method effectively captures both low-frequency global structures and high-frequency local details, overcoming limitations of fixed sinusoidal bases (e.g., poor flexibility) and pure network architecture optimizations (e.g., neglect of frequency patterns).\n3. Optimized Compression Pipeline: The \"mergeable-basis\" property enables consolidating shared structures in multi-frame compression, reducing redundancy and improving efficiency.\n4. Strong Empirical Performance: Outperforms SOTA methods on benchmarks:\nIn SR, achieves higher PSNR/SSIM across datasets (e.g., Set5, Urban100).\nIn compression, delivers significant BD-rate reductions (e.g., -21.09% vs. VTM for single-image, -20.97% for multi-image with M=24).\nCross-Task Prior Integration: Leverages pre-trained SR models as priors for image compression, enhancing information recovery.\n\nWeaknesses\n1. Computational Efficiency: The method requires optimization for computation-constrained scenarios (e.g., real-time decoding) due to higher model complexity (e.g., larger parameters and MACs compared to some baselines, as shown in Table 1 and 2).\n2. Lack of Semantic Information: The framework does not incorporate semantic understanding, which could limit performance in tasks requiring context-aware detail preservation.\n3. Scalability Challenges in Multi-Frame Compression: While merging bases improves efficiency, distortion increases slightly as the number of merged frames (M) grows, stretching basis capacity.\n4. Dependence on Backbone Architecture: Performance gains rely on integrating with strong backbones (e.g., HAT, DAT), which may limit applicability to lightweight models.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for their thorough and constructive feedback. We are encouraged that they find our paper \"interesting\" and acknowledge our contributions, including unified representation, explicit frequency modeling, optimized compression pipeline, and strong empirical performance. Below, we address each concern:\n\n\n\n> **W1. Computational Efficiency**\n    \nWe acknowledge this important practical concern. In Table 1, only the parameter count of our HAT-F is slightly more than its counterpart, HAT-L; the MAC and Memory footprint of all our models are lower than their counterparts. In Table 2, our TCM-HAT-F-multi, though with slightly more parameters, actually achieves competitive encoding time and even the lowest decoding time of all models. \nFurthermore, to demonstrate the effectiveness of our method even under computation-constrained scenarios, we integrate our Factorized Features framework to state-of-the-art lightweight super-resolution models and observe consistent improvement.\n    \n| Method          | Latency (ms) | #FLOPs (G) | #Params (K) | Set5 PSNR / SSIM | Set14 PSNR / SSIM | B100 PSNR / SSIM | Urban100 PSNR / SSIM | Manga109 PSNR / SSIM |\n|-----------------|:------------:|:----------:|:-----------:|:----------------:|:-----------------:|:----------------:|:--------------------:|:--------------------:|\n| SwinIR-lt       | 222.9        | 63.6       | 930         | 32.44 / 0.8976   | 28.77 / 0.7858    | 27.69 / 0.7406   | 26.47 / 0.7980       | 30.92 / 0.9151       |\n| ELAN-lt         | 18.0         | 54.1       | 640         | 32.43 / 0.8975   | 28.78 / 0.7858    | 27.69 / 0.7406   | 26.54 / 0.7982       | 30.92 / 0.9150       |\n| OmniSR          | 22.5         | 50.9       | 792         | 32.49 / 0.8988   | 28.78 / 0.7859    | 27.71 / 0.7415   | 26.64 / 0.8018       | 31.02 / 0.9150       |\n| SRFormer-lt     | 287.2        | 62.8       | 873         | 32.51 / 0.8988   | 28.82 / 0.7872    | 27.73 / 0.7422   | 26.67 / 0.8032       | 31.17 / 0.9165       |\n| ATD-lt          | 189.7        | 100.1      | 769         | 32.63 / 0.8998   | 28.89 / 0.7886    | 27.79 / 0.7440   | 26.97 / 0.8107       | 31.48 / 0.9198       |\n| HiT-SRF         | 82.1         | 58.0       | 866         | 32.55 / 0.8999   | 28.87 / 0.7880    | 27.75 / 0.7432   | 26.80 / 0.8069       | 31.26 / 0.9171       |\n| ASID-D8         | 61.8         | 49.6†      | 748         | 32.57 / 0.8990   | 28.89 / 0.7898    | 27.78 / 0.7449   | 26.89 / 0.8096       | –                    |\n| MambaIR-lt      | 55.8         | 84.6       | 924         | 32.42 / 0.8977   | 28.74 / 0.7847    | 27.68 / 0.7400   | 26.52 / 0.7983       | 30.94 / 0.9135       |\n| MambaIRV2-lt    | 153.4        | 75.6       | 790         | 32.51 / 0.8992   | 28.84 / 0.7878    | 27.75 / 0.7426   | 26.82 / 0.8079       | 31.24 / 0.9182       |\n| RDN             | 66.0         | 1309.2     | 22271  | 32.47 / 0.8990   | 28.81 / 0.7871    | 27.72 / 0.7419   | 26.61 / 0.8028       | 31.00 / 0.9151       |\n| RCAN            | 52.2         | 917.6      | 15592       | 32.63 / 0.9002   | 28.87 / 0.7889    | 27.77 / 0.7436   | 26.82 / 0.8087       | 31.22 / 0.9173       |\n| CATANet[1] (CVPR'25) | 102.4      | 49.3       | 535         | 32.58 / 0.8998   | 28.90 / 0.7880    | 27.75 / 0.7427   | 26.87 / 0.8081       | 31.31 / 0.9183       |\n| ESC[2] (ICCV'25)     | 21.9       | 149.2      | 968         | 32.68 / 0.9011   | 28.93 / 0.7902    | 27.80 / 0.7447   | 27.07 / 0.8144       | 31.54 / 0.9207       |\n| CATANet-F (Ours)  | 110.3      | 56.7       | 941         | 32.69 / 0.9017   | 28.93 / 0.7906    | 27.82 / 0.7444   | 27.05 / 0.8133       | 31.62 / 0.9214       |\n| ESC-F (Ours)      | 24.6       | 73.4       | 952         | 32.74 / 0.9032   | 28.99 / 0.7931    | 27.86 / 0.7483   | 27.11 / 0.8158       | 31.78 / 0.9233       |\n\n[1] Liu, X., Liu, J., Tang, J., & Wu, G. (2025). CATANet: Efficient Content-Aware Token Aggregation for Lightweight Image Super-Resolution. In Proceedings of the Computer Vision and Pattern Recognition Conference (pp. 17902-17912).\n\n[2] Lee, D., Yun, S., & Ro, Y. (2025). Emulating Self-attention with Convolution for Efficient Image Super-Resolution. arXiv preprint arXiv:2503.06671.\n\n> **W2. Lack of Semantic Information**\n\nGood catch! Our current focus is on frequency-domain structural modeling rather than semantic understanding. However, our framework is extensible - for example, we can insert the CLIP feature into the Coefficient Backbone [3] or condition attention on human instructions [4] in the Basis Transformer for explicit guidance. We will leave this to future work.\n\n[3] Lu, Z., Xia, Q., Wang, W., & Wang, F. (2025). CLIP-aware domain-adaptive super-resolution. Multimedia Systems, 31(3), 257.\n\n[4] Conde, M. V., Geigle, G., & Timofte, R. (2024, September). Instructir: High-quality image restoration following human instructions. In European Conference on Computer Vision (pp. 1-21). Cham: Springer Nature Switzerland.\n    \n\n> **W3. Scalability in Multi-Frame Compression**\n\nAs shown in Figure 7, our method demonstrates robust scalability. The PSNR remains high even at M=24, with only a minor degradation of approximately 0.1 dB when increasing M from 8 to 24. This slight quality loss, resulting from more frames sharing common bases, is significantly outweighed by the twofold improvement in compression efficiency. This trade-off is more favorable than those offered by existing methods.\n\nRegarding Table 2, the high BD-Rate observed at small values of M (e.g., M=1) is attributed to the overhead from the additional basis transmission branch, as detailed in Figure 10 of the Supplement.\n\n> **W4. Backbone Architecture Dependence**\n\nWe integrate our Factorized Features framework into state-of-the-art lightweight super-resolution models and witness consistent improvement as shown in the table of W1.\n   \n> **Q1. Failure Cases**\n\nFailure cases typically involve extremely fine textures—details that are absent in the low-resolution (LR) input but appear in the super-resolved (SR) output. However, this has been a shared inherent limitation of super-resolution methods to date. For example, in the top row of Figure 6, some white structures are present in HR but are completely absent in LR.\n\nNote that due to rebuttal guidelines, we can not include images or external links here; visual examples of these failure cases will be provided in the revised manuscript.\n    \n> **L1. Task-Specific Overfitting**\n\nWe thank the reviewer for this question. We understand it to ask whether our Factorized Features overfit to a single task or dataset. In fact, they exhibit strong cross-task and cross-domain generalization. For example, the same Factorized Features learned for super-resolution transfer seamlessly to image compression (as described in Section 4.3) and other low-level vision tasks such as image restoration (see below). \n\nEven within super-resolution, a model trained exclusively on the DF2K dataset achieves excellent performance on held-out benchmarks (the lightweight SR comparison Table in Question 1 is trained with DF2K). If this does not address your concern, could you please clarify further?\n\n#### GoPro Dataset (Motion Deblurring)\n| Metric / Method  | DeblurGAN-v2 | SRN  | DMPHN | SDWNet | MPRNet | MIMO-UNet+ | DeepRFT+ | MAXIM-3S | Stripformer | MSDI-net | Restormer | NAFNet | FFTformer | GRL-B | MLWNet (CVPR'24) | MLWNet-F |\n|------------------|--------------|------|-------|--------|--------|------------|----------|----------|-------------|----------|-----------|--------|-----------|-------| ---------------- | -------- |\n| **PSNR**         | 29.55        | 30.26| 31.20 | 31.26  | 32.66  | 32.45      | 33.23    | 32.86    | 33.08       | 33.28    | 33.57     | 33.69  | 34.21     | 33.93 | 33.83            | 34.4     |\n| **SSIM**         | 0.934        | 0.934| 0.945 | 0.966  | 0.959  | 0.957      | 0.963    | 0.961    | 0.962       | 0.964    | 0.966     | 0.967  | 0.969     | 0.968 | 0.968            | 0.971    |\n#### Dense-Haze Dataset (Dehazing)\n| Metric / Method | DehazeNet | AOD-Net | MSBDN | FFA-Net | AECR-Net | DeHamer | PMNet | DehazeFormer | TaylorFormer | LH-Net | MITNet | PGH^2Net (AAAI'24) | ConvIR (TPAMI'24) | ConvIR-F|\n|-----------------|-----------|---------|-------|---------|----------|---------|-------|--------------|--------------|--------|--------|-----------         | ---               | --      |\n| **PSNR**        | 13.84     | 13.14   | 15.37 | 14.39   | 15.80    | 16.62   | 16.79 | 16.29        | 16.66        | 18.87  | 16.97  | 17.02              | 17.45             | 18.12   |\n| **SSIM**        | 0.43      | 0.41    | 0.49  | 0.45    | 0.47     | 0.56    | 0.51  | 0.51         | 0.56         | 0.561  | 0.606  | 0.61               | 0.802             | 0.823   |\n\n#### Our framework clearly generalizes across diverse low-level vision tasks. Due to time constraints in the rebuttal phase, we have focused on these two additional benchmarks, but we will include further evaluations on denoising, deraining, and other tasks in the revised manuscript.\n\n> **S&W1. Generalization**\n\nWe can indeed extend our network to other tasks. For image generation, for example, we can integrate our Factorized Features into the VAE decoder of a diffusion model. For video generation, we can employ our mergeable basis and leverage its properties to enhance structural coherence. We will discuss these extensions in the Future Work / Directions section.\n\nWe hope these clarifications address the reviewer's concerns. We believe the strong empirical results, unified framework, and extensibility of our approach constitute significant contributions that merit acceptance. We will incorporate all suggested improvements in the final version."}, {"review_id": "Qjv62HDaKO", "reviewer": "Reviewer_Wt2E", "summary": "FIPER introduces factorized features, which can be used for low-level vision tasks such as super-resolution and image compression. Unlike previous works, FIPER decomposes features into basis and coefficients while explicitly modelling frequency components. It replaces standard feature maps and demonstrates strong generalization across both tasks. Experiments show significant performance improvement for both super-resolution and image compression tasks.", "questions": "Could you report results (accuracy and runtime) with a lightweight CNN or Mobile-ViT backbone to demonstrate wider applicability?\n\nWhy choose N = 6 coefficient–basis pairs and alpha ∈ {1, 4, 16, 64}?  An ablation on N and frequency counts would help\n\nFigure 3 lacks clarity, as the results for the toy example appear identical across all cases. Can you shed more light on it?\n\nWhat would be the effect if, instead of applying the coordinate transformation \\gamma to x in Equation 6, we use a sine or cosine transformation?", "limitations": "Please see weaknesses and questions", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe core contribution, leveraging a frequency-aware decomposition (basis × coefficient) across both super-resolution and image compression, is well motivated and novel.\n\nThe paper reports significant improvements over prior SOTA on multiple SR benchmarks (e.g., Set5, Urban100) and achieves a 21% BD-Rate gain on image compression compared to VTM, outperforming several recent methods like TCM and ELIC.\n\n\nWeaknesses:\n\nThe method requires pre-trained strong backbones (e.g., HAT, DAT). A comparison with lightweight SR/IC methods would improve practical relevance.\n\nThe paper presents Factorized Features as a “unified representation for low-level vision,” yet experiments cover only 4× SR and image compression; no evidence is given for de-blurring, denoising, and other low-level vision tasks.", "was_revised": true, "final_justification": "The authors have addressed my questions in the rebuttal, particularly regarding the extension of their approach to other low-level vision tasks and the demonstration of its effectiveness with lightweight models. Therefore, I am inclined to recommend acceptance.", "rebuttal": "We sincerely thank the reviewer for their positive assessment and constructive feedback. We are encouraged that they find our frequency-aware decomposition \"well motivated and novel\" and acknowledge our significant improvements (21% BD-Rate gain). We address each concern below:\n\n> **W1. Lightweight Backbone Evaluation**\n\nThank you for this important suggestion. We have conducted additional experiments with lightweight backbones and observed that Factorized Features provides consistent gains even in resource-constrained settings: lightweight models can also benefit from our Factorized Features.\n| Method          | Latency (ms) | #FLOPs (G) | #Params (K) | Set5 PSNR / SSIM | Set14 PSNR / SSIM | B100 PSNR / SSIM | Urban100 PSNR / SSIM | Manga109 PSNR / SSIM |\n|-----------------|:------------:|:----------:|:-----------:|:----------------:|:-----------------:|:----------------:|:--------------------:|:--------------------:|\n| SwinIR-lt       | 222.9        | 63.6       | 930         | 32.44 / 0.8976   | 28.77 / 0.7858    | 27.69 / 0.7406   | 26.47 / 0.7980       | 30.92 / 0.9151       |\n| ELAN-lt         | 18.0         | 54.1       | 640         | 32.43 / 0.8975   | 28.78 / 0.7858    | 27.69 / 0.7406   | 26.54 / 0.7982       | 30.92 / 0.9150       |\n| OmniSR          | 22.5         | 50.9       | 792         | 32.49 / 0.8988   | 28.78 / 0.7859    | 27.71 / 0.7415   | 26.64 / 0.8018       | 31.02 / 0.9150       |\n| SRFormer-lt     | 287.2        | 62.8       | 873         | 32.51 / 0.8988   | 28.82 / 0.7872    | 27.73 / 0.7422   | 26.67 / 0.8032       | 31.17 / 0.9165       |\n| ATD-lt          | 189.7        | 100.1      | 769         | 32.63 / 0.8998   | 28.89 / 0.7886    | 27.79 / 0.7440   | 26.97 / 0.8107       | 31.48 / 0.9198       |\n| HiT-SRF         | 82.1         | 58.0       | 866         | 32.55 / 0.8999   | 28.87 / 0.7880    | 27.75 / 0.7432   | 26.80 / 0.8069       | 31.26 / 0.9171       |\n| ASID-D8         | 61.8         | 49.6†      | 748         | 32.57 / 0.8990   | 28.89 / 0.7898    | 27.78 / 0.7449   | 26.89 / 0.8096       | –                    |\n| MambaIR-lt      | 55.8         | 84.6       | 924         | 32.42 / 0.8977   | 28.74 / 0.7847    | 27.68 / 0.7400   | 26.52 / 0.7983       | 30.94 / 0.9135       |\n| MambaIRV2-lt    | 153.4        | 75.6       | 790         | 32.51 / 0.8992   | 28.84 / 0.7878    | 27.75 / 0.7426   | 26.82 / 0.8079       | 31.24 / 0.9182       |\n| RDN             | 66.0         | 1309.2     | 22271       | 32.47 / 0.8990   | 28.81 / 0.7871    | 27.72 / 0.7419   | 26.61 / 0.8028       | 31.00 / 0.9151       |\n| RCAN            | 52.2         | 917.6      | 15592       | 32.63 / 0.9002   | 28.87 / 0.7889    | 27.77 / 0.7436   | 26.82 / 0.8087       | 31.22 / 0.9173       |\n| CATANet[1] (CVPR'25) | 102.4      | 49.3       | 535         | 32.58 / 0.8998   | 28.90 / 0.7880    | 27.75 / 0.7427   | 26.87 / 0.8081       | 31.31 / 0.9183       |\n| ESC[2] (ICCV'25)     | 21.9       | 149.2      | 968         | 32.68 / 0.9011   | 28.93 / 0.7902    | 27.80 / 0.7447   | 27.07 / 0.8144       | 31.54 / 0.9207       |\n| CATANet-F (Ours)  | 110.3      | 56.7       | 941         | 32.69 / 0.9017   | 28.93 / 0.7906    | 27.82 / 0.7444   | 27.05 / 0.8133       | 31.62 / 0.9214       |\n| ESC-F (Ours)      | 24.6       | 73.4       | 952         | 32.74 / 0.9032   | 28.99 / 0.7931    | 27.86 / 0.7483   | 27.11 / 0.8158       | 31.78 / 0.9233       |\n\n\nDue to time and resource constraints, we have focused on these initial evaluations on super-resolution; comparisons with lightweight image compression methods[3][4] will be included in the final version. We will add this analysis to the paper.\n\n[1] Liu, X., Liu, J., Tang, J., & Wu, G. (2025). CATANet: Efficient Content-Aware Token Aggregation for Lightweight Image Super-Resolution. In Proceedings of the Computer Vision and Pattern Recognition Conference (pp. 17902-17912).\n\n[2] Lee, D., Yun, S., & Ro, Y. (2025). Emulating Self-attention with Convolution for Efficient Image Super-Resolution. arXiv preprint arXiv:2503.06671.\n\n[3] Bao, Y., Tan, W., Jia, C., Li, M., Liang, Y., & Tian, Y. (2025). ShiftLIC: Lightweight Learned Image Compression with Spatial-Channel Shift Operations. IEEE Transactions on Circuits and Systems for Video Technology.\n\n[4] Wang, S., Cheng, Z., Feng, D., Lu, G., Song, L., & Zhang, W. (2024, December). Asymllic: Asymmetric lightweight learned image compression. In 2024 IEEE International Conference on Visual Communications and Image Processing (VCIP) (pp. 1-5). IEEE.\n\n\n> **W2. Limited Task Coverage**\n\nWe acknowledge this limitation and have extended our evaluation:\n#### GoPro Dataset (Motion Deblurring)\n| Metric / Method  | DeblurGAN-v2 | SRN  | DMPHN | SDWNet | MPRNet | MIMO-UNet+ | DeepRFT+ | MAXIM-3S | Stripformer | MSDI-net | Restormer | NAFNet | FFTformer | GRL-B | MLWNet (CVPR'24) | MLWNet-F |\n|------------------|--------------|------|-------|--------|--------|------------|----------|----------|-------------|----------|-----------|--------|-----------|-------| ---------------- | -------- |\n| **PSNR**         | 29.55        | 30.26| 31.20 | 31.26  | 32.66  | 32.45      | 33.23    | 32.86    | 33.08       | 33.28    | 33.57     | 33.69  | 34.21     | 33.93 | 33.83            | 34.4     |\n| **SSIM**         | 0.934        | 0.934| 0.945 | 0.966  | 0.959  | 0.957      | 0.963    | 0.961    | 0.962       | 0.964    | 0.966     | 0.967  | 0.969     | 0.968 | 0.968            | 0.971    |\n#### Dense-Haze Dataset (Dehazing)\n| Metric / Method | DehazeNet | AOD-Net | MSBDN | FFA-Net | AECR-Net | DeHamer | PMNet | DehazeFormer | TaylorFormer | LH-Net | MITNet | PGH^2Net (AAAI'24) | ConvIR (TPAMI'24) | ConvIR-F|\n|-----------------|-----------|---------|-------|---------|----------|---------|-------|--------------|--------------|--------|--------|-----------         | ---               | --      |\n| **PSNR**        | 13.84     | 13.14   | 15.37 | 14.39   | 15.80    | 16.62   | 16.79 | 16.29        | 16.66        | 18.87  | 16.97  | 17.02              | 17.45             | 18.12   |\n| **SSIM**        | 0.43      | 0.41    | 0.49  | 0.45    | 0.47     | 0.56    | 0.51  | 0.51         | 0.56         | 0.561  | 0.606  | 0.61               | 0.802             | 0.823   |\n\nOur framework clearly generalizes across diverse low-level vision tasks. Due to time constraints in the rebuttal phase, we have focused on these two additional benchmarks, but we will include further evaluations on denoising, deraining, and other tasks in the revised manuscript.\n\n> **Q1. Runtime with Lightweight Backbones**\n\nPlease see W1. Note that ESC is convolution-based while CATANet is a hybrid transformer.\n\n> **Q2. Hyperparameter Choices (N=6, α∈{1,4,16,64})**\n\n\n|                |     |     |     |     |     |     |     |     |\n|----------------|-----|-----|-----|-----|-----|-----|-----|-----|\n| **N**          | $1$     | $1$              | $2$              | $6$     | $6$       | $6$             | $6$                      | $10$            |\n| **$\\alpha$**   | $\\{1\\}$ | $\\{1,4,16,64\\}$  | $\\{1,4,16,64\\}$  | $\\{1\\}$ | $\\{1,4\\}$ | $\\{1,4,16,64\\}$ | $\\{1,4,16,64,256,1024\\}$ | $\\{1,4,16,64\\}$ |\n| **Set5 PSNR**  |  32.62  |   32.64          |     32.70        | 32.62   |  32.71    |  32.74          |         32.69            |     32.73       |\n| **Set5 SSIM**  |  0.9018 |   0.9020         |     0.9029       | 0.9020  |  0.9027   |  0.9032         |         0.9024           |     0.9033      |\n\nWe choose $N=6$ for better quality and training efficiency ($N=10$ converges slower).\n\n\n> **Q3. Figure 3 Clarity**\n\nFigure 3 shows the difference between vanilla fields, coordinate transformation, and multi-frequency modulation. Specifically, 3.a is a vanilla basis-coefficient field, and 3.b adds sawtooth transformation. We can see in 3.b that the coordinate transformation explicitly models a patch-like pattern, e.g., the second plot from the top is divided into two periods. By enforcing such frequency components, the models can decompose the signal effectively.\n\nNext, 3.d is our full formulation, while 3.c has no $\\alpha$. Intuitively, from 3.b to 3.c, applying $\\psi$ (we use $cos$ here) should not have much effect on the performance since we do not have any constraint on these learnable bases. With the introduction of $\\alpha$, the models are forced to attend to signal components of different frequencies. \nNote that due to rebuttal guidelines, we can not include images or external links here; we will adjust the graph layout and font for better clarity.\n\n> **Q4. Alternative Transformations**\n\nThe experiment is conducted with ESC-F as in W1.\n\n| Set5 Performance / $\\gamma$ | Sawtooth | Sin    | Triangular |\n| --------------------------- | -------- | ---    | ---------- |\n| PSNR                        | 32.71    | 32.69  |  32.71     |\n| SSIM                        | 0.9027   | 0.9026 | 0.9023     |"}, {"review_id": "dz43CjDdwd", "reviewer": "Reviewer_YrvH", "summary": "This paper proposes \"Factorized Features,\" a unified representation for low-level vision tasks, specifically demonstrating its effectiveness in Single Image Super-Resolution (SISR) and Image Compression. Unlike prior work focusing on network architecture, their approach uses a learned basis-coefficient decomposition with explicit frequency formulation to capture structural and multi-scale features. This representation is designed to generalize broadly, replacing simple feature maps in existing models. The authors further optimize image compression by leveraging a mergeable-basis property for multi-frame scenarios. Extensive experiments show state-of-the-art performance, with significant PSNR gains in SR and BD-rate reduction in image compression.", "questions": "1. For \"broad generalizability,\" the paper only evaluates on two low-level vision tasks (SISR and image compression). Expanding to other tasks like denoising, deblurring, or inpainting would further strengthen the claim.\n\n2. The Lack of ablation:\n  2.1 Could a more comprehensive ablation study be provided to quantify the individual contribution of each innovative component (e.g., presence/absence of spatially variant coefficients, learned non-uniform bases, coordinate transformation, and multi-frequency modulation) to the final performance? This would be crucial for understanding which elements are the key drivers behind the observed performance improvements.\n2.2 Could an ablation study on the choice of N (the number of frequency components) be provided? How do different values of N affect the model's performance, complexity, and its ability to capture fine image details? Is there an optimal value of N, or does it vary depending on the specific task?", "limitations": "See Questions.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength\n\n1. The concept of \"Factorized Features\" as a unified representation for diverse low-level vision tasks like SR and compression is a significant and novel contribution. This approach moves beyond purely architectural improvements to focus on fundamental image content representation.\n2. By replacing simple feature maps with Factorized Features, the paper successfully demonstrates the potential for broad generalizability across different low-level vision tasks and existing backbones.\n\n\nWeaknesses:\n\n1. While \"Learned Non-uniform Basis\" is introduced, the mechanism for generating the entire basis map  for better fitting and local reconstruction needs more in-depth explanation beyond just \"networks to generate.\"\n\n2. While a \"mergeable-basis property\" is mentioned for multi-image compression, the explanation (Eq. 10 and related text) is brief and could be expanded to clarify the practical benefits and challenges in this setup.", "was_revised": true, "final_justification": "This paper presents a novel and effective framework for content-aware basis learning, with demonstrated benefits in low-level vision tasks. The authors have provided a thorough and convincing rebuttal, addressing all raised concerns with additional explanations, ablation studies, and extended evaluations on diverse tasks such as motion deblurring and dehazing.", "rebuttal": "We sincerely thank the reviewer for recognizing our work as \"excellent\" in quality and clarity, and for acknowledging our \"significant and novel contribution.\" We address all concerns comprehensively below:\n\n> **W1. Learned Non-uniform Basis Mechanism**\n    \nIn lines 89-100 of the Supplement, we describe implementation details of how the basis is generated. To be more clear, given an image, we extract a feature $X_{coeff}$ by Coefficient Backbone, and then the Basis Transformer is applied to refine the feature with downsampling for final basis generation. After the reconstruction with the coefficient and basis, the prediction is used to compute the loss and subsequently optimize the network. With gradient descent, when the Basis Transformer is optimized, the basis is optimized simultaneously, i.e., the models are trained to adapt to content-aware basis, so the basis is not calculated by heuristic rules. This design enables **content-aware basis generation**: smooth regions get low-frequency bases while textured areas receive high-frequency ones. We will expand this explanation with architectural diagrams in the revision.\n\n\n> **W2. Mergeable-basis Property Explanation**\n\nThank you for this valuable suggestion. We will expand the discussion around Eq. 10 in the main text to clarify both the benefits and limitations of our mergeable-basis approach. Specifically:\n\nAs detailed in lines 133–141 of the Supplementary, our merged basis exploits the observation that different images often share common frequency components. By learning a single, shared set of basis functions, we can leverage the frequently appearing similar or repetitive patterns across images to greatly reduce coding redundancy in multi-image compression. In practice, this means fewer total parameters and lower computational cost required when compressing an image collection. We also note the trade-off: when images are highly diverse, forcing them into one shared basis can increase reconstruction error (as seen by the quality drop for larger M in Fig. 7). Still, this content-aware information redundancy exploitation enables a significant reduction in resource usage, and we will make these points explicit in the revised manuscript.\n\n> **Q1. Evaluation on More Tasks**\n\nWe acknowledge this limitation and have extended our evaluation:\n#### GoPro Dataset (Motion Deblurring)\n| Metric / Method  | DeblurGAN-v2 | SRN  | DMPHN | SDWNet | MPRNet | MIMO-UNet+ | DeepRFT+ | MAXIM-3S | Stripformer | MSDI-net | Restormer | NAFNet | FFTformer | GRL-B | MLWNet (CVPR'24) | MLWNet-F |\n|------------------|--------------|------|-------|--------|--------|------------|----------|----------|-------------|----------|-----------|--------|-----------|-------| ---------------- | -------- |\n| **PSNR**         | 29.55        | 30.26| 31.20 | 31.26  | 32.66  | 32.45      | 33.23    | 32.86    | 33.08       | 33.28    | 33.57     | 33.69  | 34.21     | 33.93 | 33.83            | 34.4     |\n| **SSIM**         | 0.934        | 0.934| 0.945 | 0.966  | 0.959  | 0.957      | 0.963    | 0.961    | 0.962       | 0.964    | 0.966     | 0.967  | 0.969     | 0.968 | 0.968            | 0.971    |\n#### Dense-Haze Dataset (Dehazing)\n| Metric / Method | DehazeNet | AOD-Net | MSBDN | FFA-Net | AECR-Net | DeHamer | PMNet | DehazeFormer | TaylorFormer | LH-Net | MITNet | PGH^2Net (AAAI'24) | ConvIR (TPAMI'24) | ConvIR-F|\n|-----------------|-----------|---------|-------|---------|----------|---------|-------|--------------|--------------|--------|--------|-----------         | ---               | --      |\n| **PSNR**        | 13.84     | 13.14   | 15.37 | 14.39   | 15.80    | 16.62   | 16.79 | 16.29        | 16.66        | 18.87  | 16.97  | 17.02              | 17.45             | 18.12   |\n| **SSIM**        | 0.43      | 0.41    | 0.49  | 0.45    | 0.47     | 0.56    | 0.51  | 0.51         | 0.56         | 0.561  | 0.606  | 0.61               | 0.802             | 0.823   |\n\nOur framework clearly generalizes across diverse low-level vision tasks. Due to time constraints in the rebuttal phase, we have focused on these two additional benchmarks, but we will include further evaluations on denoising, deraining, and other tasks in the revised manuscript.\n\nFuthermore, to demonstrate our method’s broader effectiveness, we integrated the Factorized Features framework into state-of-the-art lightweight super-resolution models and observed consistent performance gains.\n\n|Method|Latency_ms|#FLOPs_G|#Params_K|Set5_PSNR/SSIM|Set14_PSNR/SSIM|B100_PSNR/SSIM|Urban100_PSNR/SSIM|Manga109_PSNR/SSIM|\n|---|---|---|---|---|---|---|---|---|\n|SwinIR-lt|222.9|63.6|930|32.44/0.8976|28.77/0.7858|27.69/0.7406|26.47/0.7980|30.92/0.9151|\n|ELAN-lt|18.0|54.1|640|32.43/0.8975|28.78/0.7858|27.69/0.7406|26.54/0.7982|30.92/0.9150|\n|OmniSR|22.5|50.9|792|32.49/0.8988|28.78/0.7859|27.71/0.7415|26.64/0.8018|31.02/0.9150|\n|SRFormer-lt|287.2|62.8|873|32.51/0.8988|28.82/0.7872|27.73/0.7422|26.67/0.8032|31.17/0.9165|\n|ATD-lt|189.7|100.1|769|32.63/0.8998|28.89/0.7886|27.79/0.7440|26.97/0.8107|31.48/0.9198|\n|HiT-SRF|82.1|58.0|866|32.55/0.8999|28.87/0.7880|27.75/0.7432|26.80/0.8069|31.26/0.9171|\n|ASID-D8|61.8|49.6†|748|32.57/0.8990|28.89/0.7898|27.78/0.7449|26.89/0.8096|-|\n|MambaIR-lt|55.8|84.6|924|32.42/0.8977|28.74/0.7847|27.68/0.7400|26.52/0.7983|30.94/0.9135|\n|MambaIRV2-lt|153.4|75.6|790|32.51/0.8992|28.84/0.7878|27.75/0.7426|26.82/0.8079|31.24/0.9182|\n|RDN|66.0|1309.2|22271|32.47/0.8990|28.81/0.7871|27.72/0.7419|26.61/0.8028|31.00/0.9151|\n|RCAN|52.2|917.6|15592|32.63/0.9002|28.87/0.7889|27.77/0.7436|26.82/0.8087|31.22/0.9173|\n|CATANet[1] (CVPR'25)|102.4|49.3|535|32.58/0.8998|28.90/0.7880|27.75/0.7427|26.87/0.8081|31.31/0.9183|\n|ESC[2] (ICCV'25)|21.9|149.2|968|32.68/0.9011|28.93/0.7902|27.80/0.7447|27.07/0.8144|31.54/0.9207|\n|CATANet-F (Ours)|110.3|56.7|941|32.69/0.9017|28.93/0.7906|27.82/0.7444|27.05/0.8133|31.62/0.9214|\n|ESC-F (Ours)|24.6|73.4|952|32.74/0.9032|28.99/0.7931|27.86/0.7483|27.11/0.8158|31.78/0.9233|\n\n[1] Liu, X., Liu, J., Tang, J., & Wu, G. (2025). CATANet: Efficient Content-Aware Token Aggregation for Lightweight Image Super-Resolution. In Proceedings of the Computer Vision and Pattern Recognition Conference (pp. 17902-17912).\n\n[2] Lee, D., Yun, S., & Ro, Y. (2025). Emulating Self-attention with Convolution for Efficient Image Super-Resolution. arXiv preprint arXiv:2503.06671.\n\n\n\n\n> **Q2. Comprehensive Component Ablation**\n\nThe experiment is conducted with ESC-F as in Q1.\n\n#### Comparison of multi-frequency modulation and the number of frequency components\n\n|                |     |     |     |     |     |     |     |     |\n|----------------|-----|-----|-----|-----|-----|-----|-----|-----|\n| **N**  (the number of frequency components)          | $1$     | $1$              | $2$              | $6$     | $6$       | $6$             | $6$                      | $10$            |\n| **$\\alpha$**  (modulation frequencies)  | $\\{1\\}$ | $\\{1,4,16,64\\}$  | $\\{1,4,16,64\\}$  | $\\{1\\}$ | $\\{1,4\\}$ | $\\{1,4,16,64\\}$ | $\\{1,4,16,64,256,1024\\}$ | $\\{1,4,16,64\\}$ |\n| **Set5 PSNR**  |  32.62  |   32.64          |     32.70        | 32.62   |  32.71    |  32.74          |         32.69            |     32.73       |\n| **Set5 SSIM**  |  0.9018 |   0.9020         |     0.9029       | 0.9020  |  0.9027   |  0.9032         |         0.9024           |     0.9033      |\n\n#### Comparison of  Coordinate Transformation\n\n| Set5 Performance / $\\gamma$ | Sawtooth | Sin    | Triangular |\n| --------------------------- | -------- | ---    | ---------- |\n| PSNR                        | 32.71    | 32.69  |  32.71     |\n| SSIM                        | 0.9027   | 0.9026 | 0.9023     |\n\nWe choose $N=6$ for better quality and training efficiency ($N=10$ converges slower). Note that due to time and resource constraint we omit spatial variant coefficients since it is quite intuitive and also learned non-uniform bases since it is discussed in Figure 2."}, {"review_id": "PWc72C0Tdy", "reviewer": "Reviewer_evQ6", "summary": "1. The paper proposed a general feature decomposition method that can handle both image super resolution and compression. \n2. Instead of using fixed basis as fourier transform and wavelet transform, this paper is proposed to generate image specific basis, which help to improve the high-frequency repeating patterns recovery.\n3. Experiments show that the proposed method achieves SOTA performance on multiple benchmarks.", "questions": "1. What is z in equation (9)? And what is the R here?\n2. The learned coefficients and basis are pixel-wise, but Fourier transform is global. So how to extend equation (2) to (3) is not clear to me.\n3. In Fig. 2(b), what is the meaning of \"trainable basis settings\" here, I thought x and y are fixed.\n4. Can authors explain more about the alpha in Figure. (4)?\n5. Any visualization of the extracted high-frequency features?\n6. How to learn the k? Is it a pure scalar or the output of some conv layers.\n7. Figure 5 looks like learning the coefficients and basis in parallel. I do not fully understand why authors claimed \"our method derives the coefficient features first\"\n8. Any Coordinate Transformation tried other than Sawtooth?", "limitations": "Can authors explain more about the following limitation? \nAlthough effective, our method requires further optimization for computation-limited scenarios such as real-time decoding.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "1. The experiments are solid. Toy example in Figure 2 shows the advantage of learnable basis.\n2. The pipeline is novel, which combines the advantage of both deep network and fixed basis.\n3. The description is a bit incoherent, and sometimes hard to follow. Figures (5) lack captions, which need some captions for better understanding.\n4. Experiments show that repeating patterns can be better recovered.", "was_revised": true, "final_justification": "Based on the feedback from the authors, all of my concerns are solved and I have updated my scores.", "rebuttal": "We sincerely thank the reviewer for recognizing our solid experiments and novel pipeline. We apologize for the clarity issues and address each question comprehensively below:\n\n> **Q1. Notation in Equation (9)**\n\nWe apologize for any confusion caused by our notation. We mainly follow the notations and definitions in [1]. In Equation (9): $L = R(\\hat{y}) + R(\\hat{z}) + \\lambda\\,D(x, \\hat{x})$\n\n- **$\\hat{z}$** refers to the **hyperprior**, an auxiliary latent used to estimate the scale parameters for entropy coding, following the standard variational hyperprior framework.  \n- **$R(\\cdot)$** denotes the **bit-rate cost** of encoding a quantized variable, representing the rate term in the rate–distortion objective.\n\nThus, $R(\\hat{y}) + R(\\hat{z})$ measures the total bit cost for both the primary latents and the hyperprior, and $\\lambda\\, D(x, \\hat{x})$ balances this cost against reconstruction quality. We will clarify these definitions in the revised manuscript.\n\n[1] Ballé, Johannes, David Minnen, Saurabh Singh, Sung Jin Hwang, and Nick Johnston. \"Variational image compression with a scale hyperprior.\" ICLR 2018.\n\n\n> **Q2. Pixel-wise vs Global Transform**\n\nThank you for raising this point. In the classical Fourier representation, each frequency component is applied uniformly across the whole image: a single scalar coefficient multiplies a fixed sinusoidal pattern, so every pixel “sees” the same globally. This is powerful for capturing overall periodicity, but it cannot adapt to local variations in texture or detail.\n\nIn our Factorized Features framework, we generalize this in two key ways, trading pure global consistency for **content-aware flexibility** while retaining frequency modeling:\n\n1. **Learnable, pixel-wise basis maps**\n   Instead of a fixed sinusoid, each basis becomes a full-resolution map that can vary from one pixel to the next, so that regions with different patterns (e.g., smooth sky vs. brick wall) get different frequency accommodations.\n\n2. **Spatially-varying coefficient maps**\n   Rather than a single scalar per frequency, we produce a coefficient **map** for each basis. This allows each location to choose how strongly it uses each basis, adapting dynamically to local edge strength, texture complexity, or noise.\n\nTogether, these two changes turn the rigid global transform into a **hybrid**:\n    - It still captures multi-frequency structure (low and high frequencies) across the image,\n    - But it now **automatically adapts** to fine details and local content via learnable maps.\n\nWhy this matters\n- **Local Detail Preservation:** Regions that need more high-frequency emphasis (e.g., sharp edges) can boost those basis maps without affecting smooth regions.\n- **Task Generality:** This flexible decomposition works not only for super-resolution but also for compression (and, in principle, deblurring or denoising), since all these tasks benefit from recovering both broad structures and subtle textures.\n\nIn short, we move from “one size fits all” sinusoidal bases and scalar coefficients to a **rich, pixel-wise basis–coefficient decomposition**, which preserves the spirit of Fourier analysis while unlocking powerful local adaptation.\n\n> **Q3. Figure 2(b) Clarification**\n\nWe thank the reviewer for this question. In Fig. 2(b), “trainable basis settings” means that we enable gradient updates on the coordinate basis by setting require_grad=True for the (x,y) tensors. In other words, although initialized with fixed grid values, these coordinates become learnable parameters during training (see lines 170–171). We will clarify this point in the revised manuscript.\n    \n> **Q4. Alpha (α) in Figure 4**\n\nWe can see in Figure 4 with sawtooth transformation $\\gamma$ the feature is prompted to learn pattern from different scale in a patch-like manner, e.g. $\\gamma_2$ makes the same basis repeat four times in the grid.\nHowever, only $\\gamma$ is not enough for very fine details; therefore, we introduce $\\alpha$ and $\\psi$. Each basis is forced to accommodate both high-frequency (large $\\alpha$) and low-frequency (small $\\alpha$) components together with periodic functions $\\psi$, i.e., larger $\\alpha$ will make $\\psi$ oscillate sharper.\nTo be more general, sawtooth transformation is to form a patch-like pattern, and $\\alpha$ is to model pixel-wise high-frequency details.\n\n> **Q5. High-frequency Feature Visualization**\n\nNote that due to rebuttal guidelines, we can not include images or external links here. We will include visual examples of the extracted high-frequency feature maps in the revised version to illustrate what the network learns. \n\n> **Q6. Learning k**\n\n- **$k$**: Pure scalar hyperparameter in sawtooth transformation in line 162, where we use $\\{256, 128, 64, 32,16,8\\}$. It is not the output of convolutional layers, found empirically using a validation set and fixed throughout training.\n- **$K$**: The number of $\\alpha$. We conduct experiments to validate the setting.\n\n|                |     |     |     |     |     |     |     |     |\n|----------------|-----|-----|-----|-----|-----|-----|-----|-----|\n| **N**  (the number of frequency components)          | $1$     | $1$              | $2$              | $6$     | $6$       | $6$             | $6$                      | $10$            |\n| **$\\alpha$**  (modulation frequencies)   | $\\{1\\}$ | $\\{1,4,16,64\\}$  | $\\{1,4,16,64\\}$  | $\\{1\\}$ | $\\{1,4\\}$ | $\\{1,4,16,64\\}$ | $\\{1,4,16,64,256,1024\\}$ | $\\{1,4,16,64\\}$ |\n| **Set5 PSNR**  |  32.62  |   32.64          |     32.70        | 32.62   |  32.71    |  32.74          |         32.69            |     32.73       |\n| **Set5 SSIM**  |  0.9018 |   0.9020         |     0.9029       | 0.9020  |  0.9027   |  0.9032         |         0.9024           |     0.9033      |\n\nWe will make this explicit in the revised manuscript.\n\n> **Q7. Sequential vs Parallel Processing**\n\nAlthough the coefficient and basis branches operate in parallel, the main feature $X_{coeff}$ is extracted via the backbone network. The basis transformer then downsamples those features to construct the basis. We will rephrase the caption and accompanying text to clearly separate these two stages.\n\n> **Q8. Alternative Coordinate Transformations**\n\n| Set5 Performance / $\\gamma$ | Sawtooth | Sin    | Triangular |\n| --------------------------- | -------- | ---    | ---------- |\n| PSNR                        | 32.71    | 32.69  |  32.71     |\n| SSIM                        | 0.9027   | 0.9026 | 0.9023     |\n\n\n> **L1. Computational Limitations**\n\nThank you for asking us to clarify this point. By “computation-limited scenarios,” we refer to environments such as on-device real-time decoding where both latency and memory are severely constrained. Although our Factorized Features design already reduces parameters, FLOPs, and peak memory compared to prior methods, the extra steps of basis generation and coefficient fusion still introduce non-negligible overhead under real-time constraints. \n\nHowever, to demonstrate our method’s effectiveness even under strict computational constraints, we integrated the Factorized Features framework into state-of-the-art lightweight super-resolution models and observed consistent performance gains.\n\n|Method|Latency_ms|#FLOPs_G|#Params_K|Set5_PSNR/SSIM|Set14_PSNR/SSIM|B100_PSNR/SSIM|Urban100_PSNR/SSIM|Manga109_PSNR/SSIM|\n|---|---|---|---|---|---|---|---|---|\n|SwinIR-lt|222.9|63.6|930|32.44/0.8976|28.77/0.7858|27.69/0.7406|26.47/0.7980|30.92/0.9151|\n|ELAN-lt|18.0|54.1|640|32.43/0.8975|28.78/0.7858|27.69/0.7406|26.54/0.7982|30.92/0.9150|\n|OmniSR|22.5|50.9|792|32.49/0.8988|28.78/0.7859|27.71/0.7415|26.64/0.8018|31.02/0.9150|\n|SRFormer-lt|287.2|62.8|873|32.51/0.8988|28.82/0.7872|27.73/0.7422|26.67/0.8032|31.17/0.9165|\n|ATD-lt|189.7|100.1|769|32.63/0.8998|28.89/0.7886|27.79/0.7440|26.97/0.8107|31.48/0.9198|\n|HiT-SRF|82.1|58.0|866|32.55/0.8999|28.87/0.7880|27.75/0.7432|26.80/0.8069|31.26/0.9171|\n|ASID-D8|61.8|49.6†|748|32.57/0.8990|28.89/0.7898|27.78/0.7449|26.89/0.8096|-|\n|MambaIR-lt|55.8|84.6|924|32.42/0.8977|28.74/0.7847|27.68/0.7400|26.52/0.7983|30.94/0.9135|\n|MambaIRV2-lt|153.4|75.6|790|32.51/0.8992|28.84/0.7878|27.75/0.7426|26.82/0.8079|31.24/0.9182|\n|RDN|66.0|1309.2|22271|32.47/0.8990|28.81/0.7871|27.72/0.7419|26.61/0.8028|31.00/0.9151|\n|RCAN|52.2|917.6|15592|32.63/0.9002|28.87/0.7889|27.77/0.7436|26.82/0.8087|31.22/0.9173|\n|CATANet_CVPR25|102.4|49.3|535|32.58/0.8998|28.90/0.7880|27.75/0.7427|26.87/0.8081|31.31/0.9183|\n|ESC_ICCV25|21.9|149.2|968|32.68/0.9011|28.93/0.7902|27.80/0.7447|27.07/0.8144|31.54/0.9207|\n|CATANet-F_Ours|110.3|56.7|941|32.69/0.9017|28.93/0.7906|27.82/0.7444|27.05/0.8133|31.62/0.9214|\n|ESC-F_Ours|24.6|73.4|952|32.74/0.9032|28.99/0.7931|27.86/0.7483|27.11/0.8158|31.78/0.9233|\n\n    \n> **S&W3. Figure 5 Caption**\n    \nThank you for highlighting this point. We agree that the presentation around Figure 5 can be made more coherent, and that explicit captions will help readers follow the workflow. In the revised manuscript, we will:\n- **Clarify the narrative:** Reorganize the text in Sections 4.2 and 4.3 to present the coefficient and basis extraction steps in a clear, sequential manner.\n- **Add detailed captions:**\n> This figure illustrates how Factorized Features are used in Super-Resolution and Image Compression. (a) Given a low-resolution input image, we first extract $X_{coeff}$ feature with Coefficient Backbone. Next, we generate the basis and coefficient with Basis Swin Transformer and convolution layers, respectively, from the same $X_{coeff}$. Finally, the prediction is reconstructed by Factorized Features Reconstruction. (b) To decrease distortion in image compression, we replace the synthesis transform of the traditional learned image compression pipeline with (a) by aligning spatial resolution and latent channels.\n\n\nThese changes will ensure the description is coherent and that Figure 5 stands on its own as a self-contained illustration of our method."}]

Author rebuttal:

Meta-review: This submission presents Factorized Features, which represents an image by learning to produce both the expansion coefficient features and basis functions. With this representation, the work developed techniques for low-level vision tasks, particularly single image super-resolution and image compression, and empirical performance is shown to surpass existing approaches.

Reviewers and I appreciate the novelty of this representation framework, and the impressive empirical strength. Reviewers mentioned a few insufficiencies of the methods, primarily in the limited low-level vision task demonstration and efficiency issues, for which the authors provided more experimental results on deblurring and dehazing tasks and with light weighted models, with supportive performance. The authors also provided further clarifications of technical choices and result explanations. Overall, this paper constitutes a nice contribution to the community. I hope the authors to include the additional results and further clarifications into the final paper.
Decision: Accept (poster)