Staged and Physics-Grounded Learning Framework with Hyperintensity Prior for Pre-Contrast MRI Synthesis
Authors: Dayang Wang
Srivathsa Pasumarthi Venkata
Ajit Shankaranarayanan
Greg Zaharchuk
Venue: ICML 2025 poster (2025)
Keywords: Contrast Enhanced MRI
MRI image synthesis
Deep Learning
Primary area: applications->health_medicine
TL;DR: A novel method solves a challenging problem in contrast enhanced MRI

Abstract: Contrast-enhanced MRI enhances pathological visualization but often necessitates Pre-Contrast images for accurate quantitative analysis and comparative assessment. However, Pre-Contrast images are frequently unavailable due to time, cost, or safety constraints, or they may suffer from degradation, making alignment challenging. This limitation hinders clinical diagnostics and the performance of tools requiring combined image types. To address this challenge, we propose a novel staged, physics-grounded learning framework with a hyperintensity prior to synthesize Pre-Contrast images directly from Post-Contrast MRIs. The proposed method can generate high-quality Pre-Contrast images, thus, enabling comprehensive diagnostics while reducing the need for additional imaging sessions, costs, and patient risks. To the best of our knowledge, this is the first Pre-Contrast synthesis model capable of generating images that may be interchangeably used with standard-of-care Pre-Contrast images. Extensive evaluations across multiple datasets, sites, anatomies, and downstream tasks demonstrate the model’s robustness and clinical applicability, positioning it as a valuable tool for contrast-enhanced MRI workflows.

Staged and Physics-Grounder Learning Framework with Hyperintensity Prior for Pre-Contrast MRI Synthesis
Dayang Wang" 1 Srivathsa Pasumarthi !
Ajit Shankaranarayanan
Greg Zaharchuk
Abstract
Similation
Low-dose
PraeDontteet
Vixzing'
Pro
Simduaton
Contrast-enhancee MRI enhances pathological visualization but often necessitates Pre-Contrast images for accurate quantitative analysis and com- parative assessment. However, Pre-Contrast im- ages are frequently unavailable due time, cost, safety constraints, or they may suffer from degradation, making alignment challenging. This limitation hinders clinical diagnostics and the performance of tools requiring combined image types. To address this challenge, we propose a novel staged,
Diagnosis
Diegnosis
Doee Enhance
Image Synthesid
Erhanos
Fost Contrast
Poet-Contrest
Clinical Settings
Synthesis Assitance
grounded learning frame- work with hyperintensity prior synthesize Pre-Contrast images directly from Post-Contrast MRIs. The proposed method can generate high- quality Pre-C Contrast images, thus, enabling com- prehensive diagnostics while reducing the need for additional imaging sessions, costs, and patient risks. To the best of our knowledge, this the first Pre-Contrass synthesis model capable of gen- erating images that may be interchangeably used with Handarddoffcal Pre-Contrast images. Ex- tensive evaluations across multiple datasets, sites, anatomies, and downstream tasks demonstrate the model's s robustness and clinical applicability, posi- tioning as valuable tool for contrast-enhanced MRI workflows.
Figure I. (A). Utilization of both Pre-Contrast and Post-Contrast images clinical workflows. (B). Challenges arise when Pre- Contrast images missing or significantly corrupted. (C). Syn- thesized images enable the successful completion of these tasks.
enhanced visualization of specific structures, Pre-Contrast images are often required for comparative assessment, base- line evaluation, and quantitative analysis. For example, Pre-Contrast image used as an inevitable reference for the brain tumor imaging starting from diagnosis, through therapy planning, to treatment response and/or recurrence assessment (Villanueva-Meyee et al., 2017; Martucci et al., 2023). Zheng et. al. proposed a 4D deep learning model leveraging Pre-Contrast, arterial, and portal venous phases of dynamic contrast enhanced MRI to improve hepatocellu- lar carcinoma lesion segmentation (Zheng al., 2022). In clinical practice, Pre- and Post-Contrast images are typical used in combined fashion for real settings such low dose simulations (Sourbron & Buckley, 2011; Wang et al., 2023), diagnosis (Villanueva-Meyee et al., 2017; Zheng et al., 2022), dose enhancement (Bône et al., 2022; Subedi et al., 2012; OCHI et al., 2014; Pasumarthi et al., 2021), etc. as shown in Fig. 1(A).
1. Introduction
Contrast enhanced Magnetic Resonance Imaging (MRI) is a critical tool in clinical diagnostics. widely used to highlight pathological regions such as tumors, lesions, and vascular abnormalities. While Post-Contrast images provide
"Equal contribution 'Sublle Medical, 883 Santa Cruz Ave Suite 205, Menlo Park, CA. 94025 *Department of Neuroradiology. Stanford University. 1201 Welch Rd, MC 5488, Stanford, CA. 94305. Correspondence Wang <dayang @ddeyng@eutlemmmtiallllcloocmmc subtlemedical.com.. Srivathsa Pasumarthi amf@subllemedical.cmm.
However, as shown in Fig. I(B), Pre-Contrast images are of- ten unavailable severely degraded due to various factors, including motion, aliasing, and streaking artifacts caused by patient movement or technical issues during data acquisition (Zaitsev et al., 2015; Graves & Mitchell, 2013). These chal- lenges hinder the reliability and quality of imaging, which can subsequently affect diagnostic accuracy and clinical
Dayang
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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decision-makinn (Cui et al., 2023). Addressing this limita- tion is critical, especially for advanced imaging modalities where Pre-Contrast images are integral to procedures like quantitative parameter mapping or contrast agent enhance- ment analysis.
ing framework that incorporates hyperintensity priors, paving the way for future advancements.
We extend our model with a variant capable of lever- aging information from comrupted images, further hancing synthesis results.
To address this issue, a natural thought is to synthesize Pre-Contrast images directly from Post-Contrast images. Nevertheless, directly training a simple image-to-image syn- thesis network (e.g. UNet (Ronneberger al., 2015)) to map Post-Contrast to Pre-Contrast images often fails to bal- ance the synthesis of the structural and contrast information in the image. Contrast agent uptake introduces non-linear changes in tissue intensity, which are further influenced by variations in relaxation times (T1 and T2) and anatomical structure (Sourbron & Buckley, 201 1). As result, naive methods tend produce blurry unrealistic reconstruc- tions that lack the fine-grained details necessary for clinical sacision-making. Due to these difficulties, progress in this field has been limited, Xue et. al. proposed the first bi- directional Post-to-Pre Contrast image synthesis model with an information disentanglement design (Xue et al., 2022). However, their methods generate very blurring and distorted contrast details, making unuseful for clinical applications. To date, no learning framework has demonstrated the abil- ity to consistently synthesize rre-Contrast images with the high quality and structural accuracy required for clinical applications.
The proposed methods are extensively evaluated on two real- world datasets collected from two hospi- tals, demonstrating their robustness.
We conduct comprehensive downstream experiments to validate the utility of the synthesized images for clinical applications.
2. Methods
In this paper, we propose Staged and PHysics-rrounded learning framework with hypErintensity prioR for Pre- Contrast MRI synthEsis (SPHERE). The proposed model features a novel dual-staged learning including uptake seg- mentation and inpainting processes. Our proposed method is well golundeoddd in MRI physies and is theorically sup- ported. This two-stage design ensures a physics-informed and structured methodology for synthesizing Pre-Contras MRI with hyperintensity priors.
2.1. Mathematical Derivation for Pre-Contrast MRI Synthesis
As unique solution to this problem, we propose the first MRI physics guided framework capable of synthesizing Pre-Contrast MRI images with exceptionally high qual- ity. Our approach integrates brightness-aware segmen- tation module, leveraging contrast agent uptake dynamics, with an advanced inpainting** learning design for accurate Pre-Contrast reconstruction. The segmentation module em- ploys soft-thresholding to isolate contrast-enhanced regions, guided by the relationship between uptake and tissue in- tensity, and constrains the inpainting+ process to ensure realistic synthesis. By explicitly modeling contrast enhance- ment dynamics, our method addresses the limitations of direct mappings and achieves an unprecedented level of per- formance in Pre-Cos Contrast image synthesis. The contribution this paper is summarized as follows:
2.1.1. I. MODEL DERIVATION
The contrast-enhanced magnetic resonance imaging (CE- MRI) is commonly performed with spoiled gradient-recalled echo (SPGR) sequence. The signal intensity of the Post- Contrast condition at steady state is characterised as (Bern- stein, 2004):
Eprst
S Spost = p psin C
E Epost
T
where T1 T1 is Longitudinal relaxation time after contrast; Spee and S Spost are the Pre-Contrast and Post-Contrast signal intensities, respectively; is the proton density that we assume a constant value (Kwong et al., 1992); a is the flip angle of the sequence.
We present a significant advancement in MRI image synthesis by developing a method capable of generat- ing high-quality Pre-Con Contrast images to address clini- cal scenarios involving missing/corrupted data, demon- strating the value of AI for science.
Solving for Eq. 1, we have
Sport / sis((n() (()
E post
(3)
Spost cos(a:) - ss)n(a)
We identify the reason for limited progress in this area with direct image synthesis and propose a staged and physics-grounded design, coupled with staged learn-
Similarly, for desired Pre-Contrast MRI unknown, we have
Eprc
Spce = psin(a)
(4)
''' denotes difference from the traditional inpainting task.
Em
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Submission and Formatting Instructions
Eprc- = E T/
(5) reconstructing Spe- We define this as new "inpainting+' task, where the '+' signifies its distinction from traditional image inpainting. Unlike standard inpainting, which primar- ily focuses on restoring missing regions, this approach lever- ages contextual information from the masked area, ensuring a more accurate reconstruction of Pre-Contrast images.
pr psin(())
E Err
(6)
Spee (a)(aa) psin(a)
where Spe represent the signal intensity of the Pre-Contrast image. Tlppe is Longitudinal relaxation time before con-
trast.
1.2.2. COMPLEXITY ANALYSIS
The relationship between the longitudinal relaxation times before and after contrast agent administration is given by (Hathout & Jamshidi, 2012):
In typical direct learning method, we aim to approximate the mapping:
1
+ [Gd],
(7)
T1 post
T1ps
Spre
[direea (Spost).
(13)
Where 71 Longitudinal relaxivity of the specific contrast agent (related TI shortening effect). [Gd] the concen- tration of the gadolinium contrast agent. Then, we have
However, based on the physical model, Spre depends both directly on Spost and indirectly through an intermediate vari- able M:
E Epost
Epre- [Gd]
Spre finpaint- (Sposts Saeg (Sppss)
(14)
Given that the exact concentration of gadolinium-based con- trast agent ([Gd) is not explicitly known, we introduce an uptake mask, denoted as M, which is a learnable variable in our model. Here, M E [o, 1] represents the degree of contrast uptake within the tissue. Assuming that the contrast agent concentration is proportional to this uptake mask, i.e., [Gd] M. the equation can be reformulated as follows:
The segmentation function fseg introduces nonlinear spa- tial dependencies, which require complex deep learn- ing model. The reconstruction function finpannt introduces physical modeling dependencies, involving exponential and trigonometric terms. The network must optimize both seg- mentation and reconstruction in one go, which multiplies the complexity.
(9) where 3 is scaling factor. Substituting the derived expres- sions for Epre and Eposs
E post
Epsc- E -R--
This formulation results in a composite function, introduc- ing cascading dependencies. By applying the chain rule for the derivative of Spre with respect to S Spost
Sp p sin((a) Spor (
= -(sp
See Spe-psin(a) cos(())-ssn(a))
TRM
dS
aS dS
as pre
dM
(15)
dS post
ØM
dS
post
post
(10)
The derivative indicates that any small error in M propa- gates into the reconstruction function, making optimization challenging. This coupled dependency results in a multi- plicative complexity scaling, expressed as:
Rearranging the equation to solve for Spee in terms of Spest:
Spre psintes) (S 180 - Spm cus(er) pe 834 sin (nine))
Spore cos(a) (Sp))-Sppeee Spe costa)- - Reg 2n)) +p (in( (a:)
(11)
Cdirect = O (Cinpuint- Cveg)
(16)
Since only Spost is available as input, we model the uptake mask M as a function S Spont As a result, directly learning Spre from Spost using an image-to-image model becomes intractable due the composition of functions. To address this, propose decomposing the synthesis process into two cascaded stages, following the formulation derived above:
However, in our two-step learning approach, the problem is split into separate tasks of fweg and fimpaintt Each function is learned independently, and the complexity of the total process is:
Spre = finpaint= (Spost, M), M
Ssog (S poat).
(12)
Ciwo-stage = O(Cinpaint)) + O(Creg) < O(Cinguint+
C.eg)
(17)
The first stage involves learning the uptake mask M using fseg. formulated as a segmentation task. In the second stage, Impaintt utilizes Spest and M compute Eq. 11, effectively
In Appendix. C, we also provided a comparative analysis of our method against traditional learning approaches from a loss optimization perspective.
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Hyperintensity Extraction
AE(A)
Intensity Adjustment
Mask Fusion
Spm
Spar cos(s)
Spe staels) polleaa psinio)
Brightness Mask (H)
Segmentation
Inpainting+
Fused
Mask(MM)
Direct Mask (Mey)
Pre-Contrast (Spre
Stage 1: Segmentation
Stage 2: Inpainting*
Post-Contrast (S poss)
Figure 2. The architecture of the dual-staged learning framework
2.2. Decoupled Two-Stage Learning Framework
H = o(u(Spust Bb)),
(20)
2.2.1. STAGE 1: LEARNING CONTRAST MASK
The uptake mask M learning is formulated segmenta- tion task aimed identifying regions with contrast enhance- ment. The segmentation model Sseg is designed to predict M directly from p
where u controls the sensitivity of the soft threshold. 3n serves as the brightness threshold, ensuring that high- intensity regions, indicative of contrast uptake, receive higher probabilities. With y and u learnable parame- ters, the model dynamically adjusts, reducing dependence on a predefined Bo. This adaptive thresholding enhances robustness across contrast agents and anatomies, improving generalization while minimizing manual tuning.
M Seog Sposti Oseg),
(18)
where Ase represents the learnable parameters of the seg- mentation model.
Specifically, the segmentation process divided into two stages: (1) a conventional deep segmentation model to gu- ranttee model precision and robustness (e.g. NestedUNet (Zhou al., 2018)), and (2) refinement module to enhance the segmentation by focusing on regions exhibiting hyperintense signals typically associ- ated with contrast enhancement.
The final segmentation map M is obtained by combining the outputs of the standard segmentation model Magg and the hyperintensity prior H through a fusion operation:
pnperiitensity-prior-gueee
M Fuse (M H),
(21)
where Fuse(.) is x Convolution operation to combine the two masks into one.
Hyperintensity Prior To incorporate the physical constraint that contrast uptake regions exhibit higher intensity values Post-Contrast MRI, we introduce a brightness prior to guide the derivation of the mask M. This mask represents the likelihood of contrast agent uptake each pixel and is constructed using soft thresholding mechanism informed by the normalized brightness of the Post-Contrast image.
The true uptake mask M representing regions contrast enhancement, is approximated by the subtraction imaging technique (Hubbard al., 2019):
M
[ Spre T)
(22)
where T(-) is the indicator function that outputs if the con- dition is true and 0 otherwise. T is the brightness threshold to remove the background noise. The Binary Cross En- tropy (BCE) loss is employed for model training. To further regularize this relationship, penalty term
To enhance hyperintensity extraction, Spost is first processed through an autoencoder A(-), which adjusts image intensity for improved contrast representation. The output is then scaled by a learnable factor y, resulting
Rhyper Σ
M - (u(() }))
(23)
post 77((Sppa)
(19)
is introduced, enforcing adherence to the prior.
where normalization ensures consistency across varying image brightness ranges. The processed intensity Syma is then mapped to the hyperintensity mask H using a Softmax function (()):
2.2.2. STAGE 2: LEARNING THE INPAINTING+ PROCESS
Using the predicted mask M and Speat- the inpainting+ model finpaint synthesizes the Spr which defined Eq.

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Sps x (1 M)
structural and contrast information. Three decoders (D1, D2, D3) are then used to reconstruct the structural domain, contrast domain, and complete image domain, respectively. For the corrupted Pre-Contrast image SAn, an initial refine- ment is performed using an encoder-decoder architecture. Subsequently, San undergoes the same decomposition and reconstruction process as Spre. Finally, a dedicated skip con- nection is incorporated merge the structural information from Spre with the refined contrast information from SAn. generating the final prediction of the Pre- Fre-Contrast image.
E1
Seuchial inlomaiion
D3
Spe
Prediction- SPHERE yeo
D2
Sye X M
Contrect Information
D1
San (1 M)
1e Refheemnt
Stecituel Information
D3
SAnt
Pre-Artifact 1Sxa!
SAn x M
Contrazt Information
Pre-Contrast Spe)
Inference
A major challenge lies in effectively disentangling structural and contrast information. To ensure robust decomposition and fusion, our model incorporates the seven routes with L1 and SSIM losses. These outputs are meticulously designed to guide the separation of structural and contrast components while promoting their synergistic integration.
Figure 3. The workflow of the SPHERE-Ar for artifact correction with the corrupted image. generates seven outputs that map to corresponding images.
11:
3. Experiments and Results
Spre
Simpaiat+ (Spost. M; impaaitt))
(24)
With IRB approval and informed consent, we ret- rospectively collected 126 cases from Site A (Gadoterate meglumine, 113 training, 13 testing) and 159 cases from Site B (Gadobenate dimeglumine, 149 training. 10 test- ing). Tab. provides cohort details. Clinical indications included suspected tumors, post-operative follow-ups, and routine brain imaging. Each patient had paired 3D T1- weighted MPRAGE seans for Pre-Contrast, Low-Dose, and Post-Contrast imaging. Images were mean mean-normalized and afgine-registered, using SimpleElastix (Marstal et al., 2016), with the Pre-Contrast image as the reference.
Dataset:
where Ompaint are the learnable parameters.
The training loss for the inpainting process is combination of L1, Structural Similarity Index (SSIM), perceptual, and adversarial losses. The L. loss minimizes the absolute pixel-wise diffcrence; SSIM Loss penalizes deviations in image structure; Perceptual loss compares the high-level features extracted from pretrained network (e.g., VGG): The adversarial loss refine the image realism. The detailed equations for all losses are listed in Appendix. B.
2.3. Adaption Artifact Removal
Table 1. Dataset cohort description
Field
TE
Flip
The proposed SPHERE model targets the synthesis of Pre- Contrast images from Post-Contrast images, specifically addressing scenarios where data is missing or corrupted due to heavy motion, aliasing, or zipper artifacts. In some instances, even structurally degraded Pre-Contrast images may still contain valuable information that can be leveraged to enhance the synthesis process. This scenario can also be viewed an artifact removal task (Cui et al., 2023; Zaitsev et al., 2015), where the desired Pre-Contrast images exist in a compromised form.
Site
Cases
Gender
Age
Scamner
Strength
(sec)
(4nc)
Angle
Site
176
55 Females
71 Males
48 + 16
Insignia
Philips
ST
2.97-3111
6.41-6.70
Site
159
X1 Males
Females
52 +
Diseowary
ST
2.99-5.17 7.73-12:25
8-20
Implementation details: All experiments were conducted with four NVIDIA A100 40GB GPU on Intel(R) Xeon(R) CPU E5-2698 v4. The base models of SPHERE used for seg- mentation, autoencoder, and inpainting+ are all NestedUNet (Zhou et al., 2018) models. To benchmark SPHERE against state-of-the--at methods, we compare its performance with UNet (Ronneberger et al., 2015), ATT-UNet (Oktay et al., 2018), NestedUNet (Zhou et al., 2018), SwinIR (Liang et al., 2021), UKAN (Li et al., 2024), MambalR (Guo et al., 2025), and BICEPS (Xue et al., 2022). These methods represent the golden standard approaches in image enhancement, seg- mentation, and synthesis. Each model was trained using its official codes, with hyperparameters such as learning rate, batch size, and loss weights fine-tuned to achieve optimal performance.
To handle such cases, we introduce an artifact removal vari- ant of SPHERE, refered to as SPHERE-Art, designed to ef- fectively extract and integrate useful information from both synthesized and corrupted images. Since the synthesized Pre-Contrass images provide accurate structural representa- tions, we focus on leveraging contrast information from the corrupted images. The architecture of this enhanced model is shown in Fig. 3.
For the synthesized Pre-Contrast image Spee we employ an encoder E₁ to decompose its manifold representation into
Several metrics are employed to quantitatively evaluate im-
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age quality, including Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM); Contrast-to- Noise Ratio (CNR), and Learned Perceptual Image Patch Similarity (LPIPS) (Zhang et al., 2018). PSNR quantifies image fidelity by comparing signal strength to noise, while SSIM assesses structural similarity between images. CNR evaluates contrast relative to background noise, particularly in regions of interest, and LPIPS leverages deep learning to measure perceptual similarity in feature space.
3.1. Comparative Results
Qualitative results in Fig. show that all existing mod- els contribute Pre-Contrast image synthesis, producing images that visually resemble the target. However, these methods struggle to balance structural and contrast infor- mation, leading to inaccuracies in fine details. In contrast, the proposed SPHERE model demonstrates superior perfor- mance across both datasets. As shown Fig. 4(A1, A2), SPHERE accurately reconstructs contrast-enhanced regions, even in small structures like the choroid plexus, where other methods fail. Additionally, SPHERE preserves structural details highly consistent with the input images, sometimes even surpassing standard-of-care (SOC) Pre-Contrast im- ages due to alignment or tissue dynamics between acqui- sitions. Similarly, Fig. 4(B1, B2) highlights SPHERE's ability to synthesize tumor structures with high fidelity, out- performing competing methods.
Figure 4. The comparative results of representative slices for dif- ferent methods. (A1,A2) are two representative slices from Site A; (B1,B2) are another two slices from Site B.
achieves the closest intensity match to the SOC Pre-Contrast image, whereas other methods exhibit significant structural inconsistencies. Additionally, the Noise Power Spectrum (NPS) analysis confirms that SPHERE produces the lowest noise levels among all compared methods. Quantitative eval- uation in Tab. further validates the superior performance of SPHERE across all contrast metrics, demonstrating its effectiveness in reconstructing contrast region while main- taining high structural accuracy.
Further validation is provided in Appendix Fig. 9, where SPHERE achieves the closest line profile relative to the true Pre-Contrast image. Quantitative results in Tab. 2 con- firm SPHERE's s superiority, achieving the highest scores across four image quality metrics on two datasets. Although advanced models like SwinIR, UKAN, and MambalR con- tribute this task, they fall short due the limitations of direct learning (discussed in Section C). In summary, SPHERE is the only model capable of generating high- quality Pre-Contrast images with precise contrast and struc- tural details, from small structures like the choroid plexus to large pathological regions such as tumors.
3.2. Motion Artifact Removal
Models from the UNet family are widely used as backbone architectures for MRI artifact removal, addressing motion artifacts, aliasing, and ringing artifacts (Yang et al., 2017: 7: Chen et al., 2023; Kang & Lee, 2024). To comprehensively evaluate the SPHERE-AN framework, we compared it with state-of-the-art UNet-based models, including UNet (Ron- neberger et al., 2015), R2-AuUNet (Alom et al., 2018), and NestedUNet (Zhou et al., 2018). For these baselines, both Post- cost-Contrast images and corrupted Pre- Pre-Contrast images were used as inputs to predict clean Pre-Contrast images.
Contrast information Evaluations
To further assess the accuracy and consistency of synthe- sized contrast in medical images, we implemented set of metrics designed to evaluate contrast preservation, fi- delity, and structural integrity within the region of interest (ROI), as defined in Eq. 22. Specifically, four metrics were employed for contrast region evaluation: Contrast Fidelity Score (CFS), Gradient Magnitude Similarity Devia- tion (GMSD), Intensity Range Consistency (IRC), and Edge Intensity Similarity (EIS). The mathematical formulations of these metrics are detailed in Appendix A.
As shown in Fig. 6, all models demonstrate some ability to reduce artifacts, but SPHERE-Art consistently outperforms them, achieving superior artifact correction across all tested scenarios. While residual artifacts remain in other methods, SPHERE-Ait reconstructs cleaner images with minimal dis- tortions. Tab. 3 further validates SPHERE-Art effective- ness, achieving the highest performance scores across all metrics. These results highlight the advantage of domain- specific knowledge integration and the dual-stage learning
As shown in Fig. 5(A), the proposed SPHERE model
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Submission and Formatting Instructions
Post Contrast
UNet
Att- UNtt
NestedUUNet
Swin
UKAN
MambalR
BICEPS
SPHERE
Pre-Core ConCrastt
(A1)
(A2)
(B1)
(B2)
Figure 5. The contrast uptake of the representative results from Site A and B; The corresponding NPS maps for each method.
Table 2. Quantitative evaluation results of different base methods on the test cases. Bold-faced numbers indicate the best results.
Site A
Site B
Method
PSNR (dB)
SSIM
CNR.
LPIPS
PSNR (dByt
SSIM
CNR
LPIPS_
UNet
34.6430 1: 0.22
0.8633 1 0.004
0.0819 = 0.002
0.0497 = 0.002
32.8615 = 0.24
0.8943 + 0.004
0.0920 1 0.002
0.0621 1 0.002
Att-UNet
34,8340 +: 0.18
0.8658 + 0.003
0.0804
0.001
0.0507 = 0.001
32.8775 = 0.16
0.8969 + 0.003
0.0906 + 0.001
0.0628 1: 0.002
UNet++
34.5522 + 0.10
0.8580 + 0.003
0.0836
0.001
0.0479 = 0.002
32.9857 = 0.14
0,9002 + 0.003
0.0909 + 0.001
0.0505 +: 0.001
SwinIR
32.7531
:
0.8124 + 0.004
0.1063
0.002
0.0660 = 0.002
31,3174 = 0,21
0.8618 + 0.004
0.1143 + 0.002
0.0679 1 0.002
UKAN
19.057411..3
0.7833 + 0.005
0.0990
0.002
0.0736 = 0.002
24.1449 : 0.34
0.6716 = 0.005
0.1408 + 0.002
0.1148 1 0.002
MambalR
32,0594 + 0.29
08813 + 0.004
0.1073
0.002
0.0867 + 0.002
29.7819 + 0.29
0.8151 + 0.004
0.1375 + 0.002
0.1121 0.002
BICEPS
35.2499 +: 0.23
0.8735 +: 0.004
0.0751
0.001
0.0397 + 0.001
34,5037
-: 0.19
0.9122 + 0.003
0.0772 +: 0.001
0.0381 + 0.001
SPHERE*
36,8244 0.14
0,9026 1: 0.002
0.001 0.0628
0.0313 = 0.001
35.3617 =: 0.15
0.9263 +: 0.001
0.0699 1 0.002
0,0330 1 0.001
Method
GMSD 1.
CFSt
IRCT
EIS
GMSD 4
CFST
IRCT
EIST
UNet
0.0360 + 0.002
0.8581 + 0.005
0.8069
0.009
0.3886 + 0.007
0.0265 + 0.001
0.7394 + 0.005
0.5747 + 0.008
0,2183 + 0.009
AttUUNet
0.0367 + 0.003
0.8641 + 0.005
0.7976
0.008
0.3765 + 0.012
0.0256 0.002
0.8633 + 0.004
0.7013 + 0.009
0.2151 + 0.014
UNet++
0.0362 + 0.003
0.8462 + 0.005
0.8454 = 0.007
0.3746 = 0.007
0.0258 : 0.002
0,8441 + 0.005
0.6547 + 0.007
0,2389 1: 0.010
SwinIR
0.0402 + 0.003
0.6081 + 0.005
0.6675 = 0.010
0.2821 = 0.015
0.0326 = 0.003
0,7421 + 0.005
0.3350 +: 0.012
0.0290 +: 0.013
UKAN
0.0601 + 0.003
0.2937 + 0.005
0.0002 0.010
0,2339 = 0.016
0.0777 : 0.004
-0.7269 0.006
-1.2471 0.012
00037710000
ManbalR
0.0441 + 0.002
0.4989 + 0.004
0.5902
0.009
0,1886 = 0.015
0.0403 1 0.002
0,8164 + 0.003
-0.0469 0.009
-0.0696 0.014
BICEPS
0.0349 0.002
0.8857 + 0.002
0.8335
0.005
0.4253 + 0.006
0.0241
0.002
0.8595 + 0.002
0.8040 + 0.005
0.3619 0.007
SPHERE*
0.0315 1 0.001
0,9181 + 0.002
0,8684 0.006
0,5364 = 0.005
0.0221 + 0.001
0.8803 - 0.002
0,8410 + 0.005
0,4433 1 0.005
key downstream tasks, including dose simulation, contrast enhancement, and applications in spine and breast imaging. All these tasks are essential for contrast-enhanced MRI applications.
Table Quantitative evaluation results of different base methods artifacts removal. Bold-faced numbers indicate the best results.
Method
PSNR (dB))
SSIM
RMSEL
CNR
LIPIPS L
Pre-Artifact
72.7499
0.1089
0.1167
0.3617
0.0298
UNet
33.4898
0.8839
0.0213
0.0566
0.0390
Low Dose Simulation: Low-dose simulation is critical task for data augmentation and optimizing radiation ex- posure in clinical settings, adhering to the 'As Low As Reasonably Achievable' (ALARA) principle (Sourbron Buckley, 2; Wang et al., 2023). This process enables the determination of the minimal effective contrast agent dosage, improving patient safety while preserving diagnos- tic quality. Low-dose simulations are performed using both Pre-Contrast and Post-Contrast images. The quantitative evaluations reveal that using synthesized Pre-Contrast im- ages deliver results comparable to using SOC Pre-Contrast
R2-AnUNct
33.5804
0.8908
0.0210
0.0557
0.0308
NestedUNct
33.0154
0.8761
0.0225
0.0592
0.0304
SPHERE-AR"
37.1245
0.9063
0,0226
0.0612
0.0298
framework, positioning SPHERE-Art as leading approach for artifact removal in clinical MRI applications.
4. Downstreaming Tasks
To further evaluate the clinical significance and quality of the synthesized Pre-Contrast images, we assess their impact on

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Submission and Formatting Instructions
Pro- Artfcc
Liie
R2 ArtUNet
NestedUNct
SPHERE Art'
Pro Contrast
Figure 6. The comparative results on the artifact removal of differ- ent methods.
images. As shown in Fig. 7(A1-A4), the overall visual quality of the synthesized low-dose images closely aligns with that of the SOC-based counterparts, demonstrating the feasibility of the proposed approach in generating reliable Low-dose images for clinical applications.
Figure 7. The results of the dowmstreaming tasks. (AI) is the low-dose simulation results with sythesized Pre-Contin Controstttt; (A2) the simulation results with SOC Pre- Pre-Contrast; (A3,A4) are two comparative results on 10% dose; (B1-B3) are three slices on Spine images; (CI-C3) are slices on Breast images. (It's better to view in zoomed fashion).
Table 4. Quantitative evaluation results of different base methods on the test cases. Bold-facee numbers indicate the best results.
Tasks
Method
PSNK (day?
SSIM
RMSE,
CNR.
LIFIPS 1
Dose Simulation
Sya Pre Contras"
SOL-Pr Cop-Coetratt
37.1081
3966535
0.9630
09454
I..736
0.0336
G10215
0.038
Spine Application
36.5489
0.942
0A038
0.9466
Breast Application
Brain transforred
39.4795
08472
00525
0,1620
0.1646
pretrained model from Site A, we fine-tuned it on breast imaging data from just three cases over 10,000 training iter- ations. Qualitative results in Fig. 7 (C1-C3) show that the synthesized images closely resemble the SOC images, while quantitative results in Tab. 4 further highlight strong perfor- mance metrics, underscoring the approach's capability to enhance diagnostic quality and workflow efficiency.
Spine Application: In spine imaging, contrast-enhanced MRI assesses conditions like infections, tumors, and de- generative diseases, with Pre-Come Pre-Contrast images crucial for distinguishing normal tissue from pathological enhancement and subtle marrow changes (Breger et al., 1989; Colosimo et al., 2006). A Post-to-Pre reconstruction technique re- duces scan time, benefiting patients prone to motion arti- facts, such as the elderly and those with chronic pain. To assess the adaptability of our method, fine-tuned a pre- trained model (trained on Site A data) using limited Spine imaging dataset consisting of TI-weighted Pre-Contrast and
5. Ablation Study
In this section, we present an ablation study to assess the contribution of key components in the proposed method. Specifically, we investigate the effects of the dual-stage learning framework, the hyperintensity prior, the arbitrary segmentation branch, the autoencoder module, and the se- lection of the brightness threshold. Both the quantitative results (Tab. 5) and the qualitative findings (Fig. 8) demon- strate that each of these components plays essential role in improving model performance. In particular, the dual- stage learning strategy, hyperintensity prior, and arbitrary segmentation branch contribute significantly. Removing any of these components results in a consistent performance de- cline across multiple evaluation metrics, underscoring their
scans from five patients. As shown in Tab. 4 (quantitative) and Fig. 7(B1-B3) (qualitative), the transfer-learned model effectively synthesizes high-quality Tre-Contrast images, demonstrating strong generalization to Spine imaging.
Pre-Contrast images essential for baseline signal evaluation in contrast-enhanced Breast MRI (Mann et al., 2019; Van Nijnatten et al., 2024). However, these images often suffer from artifacts and misalignment is- sues that cannot be resolved through registration. A Post-to- Pre reconstruction approach addresses this limitation. Using
Breast Application:
8

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Submission and Formatting Instructions
Post-Conifasl
Wo Dual Stage
Hyperinteneily
Segrnentation
We Autoencuder
SPHERE
Pre-Contrast
0.08
0.08
T-00
1=0.22
0=1444
Figure 8. The results of the ablation study on the dual-stage learning framework, hyperintensity prior, arbitrary segmentation branch, autoencoder module, and the choice of brightness threshold T.
Table 5. Ablation study on different components and 7 selection results
Configuration
PSNR 1
SSIM f
CNR 1
LPIPS | GMSD
CFS
IRC
EIS f
W/o Dual Stage
34.5522
0,8580
0,0836
0,0479
0.0362
0.8462
0,8454
0.3746
W/o Hyperintensity
35.7608
0.8842
0.0729
0.0434
0.0356
0.8970
0.8252
0.4041
W/o Segmentation
36.3764
0.8951
0.0666
0.0346
0.0337
0.9068
0,8558
0.4703
W/o Autoencoder
36.6764
0.9006
0.0635
0.0321
0.0328
0.9119
0.8585
0.5075
SPHERE
36.8244
0.9026
0.0628
0,0313
0.0315
0,9181
0.8684
0,5364
Brightness threshold r selection
T 0.06
35.7835
0.8990
0.0651
0.0366
0.0320
0.9109
0.8560
0.5366
r == 0.08
36.8841
0.9034
0.0628
0.0298
0.0315
0.9179
0.8676
0,5319
r 0.10
36.8244
0.9026
0.0628
0.0313
0.0315
0.9181
0,8684
0,5364
r 0.12
36.8759
0.9035
0.0624
0.0299
0.0317
0.9167
0.8687
0,5333
T 0.14
36.7256
0,9008
0.0635
0.0313
0.0320
0.9097
0,8702
0.5246
importance within the overall framework.
to prolonged scanning, contributing to a more streamlined and patient-centered imaging process.
For the brightness threshold r. evaluated range of val- ues from 0.06 to 0.14. The results indicate that values within the studied range consistently yield strong performance with only minor variation. For instance, all tested values in this range achieve a PSNR of approximately 36.80=10.08 and an SSIM of approximately 0.0033 These findings suggest that the model is relatively robust to the specific choice of brightness threshold, thereby simplifying hyperparameter tuning and improving the method's 's general applicability.
Impact Statement
This paper presents the first MRI physics-guided framework for clinically viable Pre-Contrast image synthesis, address- ing key challenge in contrast-enhanced MRI. By generat- ing high-fidelity Pre-Contrast images, it overcomes barriers posed by missing or corrupted scans, improves workflow ef- ficiency, reduces costs, and offers transformative solution for clinical practice.
6. Conclusion
The proposed method offers a novel solution for synthesiz- ing Tre-Contrast images directly from Post-Contrast data, addressing key challenges in medical imaging where Pre- Contrast images are often unavailable, misaligned, or cor- rupted. This significant advancement enables high-accuracy Tre-Contrast synthesis, particularly excelling in reconstruct- ing large tumor regions, thus enhancing diagnostic reliabil- ity. By potentially eliminating the need for Pre-Contrast acquisition during MRI, this method reduces examination time, improving clinical efficiency in high-demand settings. Furthermore, it minimizes patient discomfort and exposure
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Submission and Formatting Instructions
Intensity Profile
Moan absolute error
UNet
Att-UNet
NettedUNet
0.025
UKAN
MambaiR
Intensity
BICEPS
0,000
SPHERE
Mcan
Pre- Contrast
0.025
0.
0.015
100
250
UNd
Aff-B8
HesteiLoWe
Swinsl
uKW
Hamballt
Rcces
SAHERE
Pre
Position
Intensity Profile
Mean absolute error
UNet
Att-UNet
NestedUNet
0.3
SwinlR
0.05
UKAN
MambalR
Mean error
Intensity
BICEPS
176
175
0.04
SPHERE
Pre-Contrast
0.0
0.02
6
50
100
150
200
250
UNet
All Litee
Westevtiite
Sienti
URAN
Mombeli
BICERS
SPHERS
Are Contrast
Position
Figure 9. The intensity profile of representative slice for different methods. The left two plots depict the line profile of a representative slice on vertical and horizontal orientations. left. two figures illustrate mean absolute errors different methods relative to the SOC Pre-C Contrast image.
Appendix
A. Contrast Evaluation Metric
Four quantitative metrics for contrast evaluation utilized:
1). Contrast Fidelity Score (CFS) measures the preservation of contrast magnitude between the ground truth and prediction.
It is defined as:
115m
CFS
(25)
1l + c
where Us and jls... are the mean intensity value of prediction and ground truth images. c a minimal value to avoid zero denominator. This metric measures differences in the mean intensities within the masked region, with higher values indicating better contrast preservation.
2). Gradient Magnitude Similarity Deviation (GMSD) measures the similarity between the gradient magnitudes of the prediction and ground truth images within the masked region. It defined as:
12

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Submission and Formatting Instructions
N N
1
2
GMSD
Ipm
)
(26)
where N' is the number of samples. ISS. and I.pr are the gradient magnitudes of the ground truth and prediction images, respectively, computed using the Sobel filter (Kanopoulos et al., 1988).
3). Intensity Range Consistency (IRC) evaluates the agreement in intensity range (AI) between the prediction and ground truth. is computed
Alg
pm A
IRC
(27)
Al
where AT = max(T) min(T) is the peak-to-peat intensity range.
4). Edge Intensity Similarity (EIS) assesses the correlation between edge intensities of the ground truth and prediction within the masked region. It is calculated using the Pearson correlation coefficient (Freedman et al., 2007):
EIS corr cs Es
(28)
where Es... and Esg.. are the edge intensity maps of the ground truth and prediction, respectively, obtained using the Sobel filter(Kanopoulos et al., 1988). EIS ranges from 1 to 1, with values closer to indicating better similarity.
B. Training Loss for the SPHERE
The training loss for the inpainting+ process is combination of L1, Structural Similarity Index (SSIM), perceptual, and adversarial losses. The LA loss minimizes the absolute difference between the predicted pre-contrast image Spre and the ground truth Spre: SSIM Loss measures the structural similarity between the predicted and ground truth images which penalizes deviations in image structure; Perceptual loss compares the high-level features of the predicted and ground truth images, extracted from a pretrained network (e.g., VGG (Simonyan & Zisserman, 2015)); The adversarial loss comes from a GAN (Goodfellow et al., 2014), where a generator predicts Spee and a discriminator D distinguishes between real Spre and fake Spee
1 Σ N
C11
Spre Spre
(2 Ug + C2)
Spm + C2)
LSSIM
(R3 + 4g + Ci)(o
+ to + C2)
(29)
Cpenceptual = Σ Ni (Spo)) oi (Spc))1
1 Σ log (D(
Cadv
N
where Cj and C2 are small value to avoid zero denominator; orpm and o3 are the variance of Spe and S; S is the covariance between the Spee and $; N, the number of feature map layers for perceptual loss calculation; Φi the network used for feature extration (VGG).
For the discriminator D:
dissc adv
N
Σ log ((prr)) + log (1 (1- D(Spp)))
(30)
In summary, the total inpainting+ loss combines all these components in the two stages with appropriate weighting factors:
Lippuintt AI. + ASSIM Spercepuu + Xads Lgen
(31)
Where λLι = 1, ASsIM = 10, Apereeptual = 0.5, and Aadv = 1 are weights to balance the contributions of different loss terms. The discriminator loss Cise is used to update the discriminator separately during adversarial training.
13

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Submission and Formatting Instructions
The segmentation stage is optimized using loss functions: LI loss for autoencoder reconstruction and BCE loss for segmentation:
La
Σ S post
Spust
N
(32)
Chcee
1
Σ Mine log(M) (1 Mimue log (1 M)].
N
Moreover, two penalty terms incorporated based on the MRI physics of the synthesis defined in Eq. 23 and 11:
1
Rhyper
M
σ (u(Sp post BBo)
N
p psin(a)
T TR S post cos(a) pe TRr sin(a) + psin((a)
(33)
R payn
N
pre
S e TRrr AM cos(a) S Spost cos(a) Pe perTraa sin(2a)
+ psin(a)
Here, 80 = 0.3, 5. we define the scale based on the common assumption that proton density p in brain ventricles (Mezer et al., 2016).
In summary, the total losses for SPHERE generator are:
Litul Amnpinnt Limpaint+ + > Lae + Abcehbee + Ahyper Rhyper + Xpsyn R Rasyn:
(34)
where Ampaint- 1, Aue 1, Ance 10, Ahyper 0.1, and Apryn 0.01. The weighting parameters were selected based the inherent characteristics of each loss function, rather than being optimized for specific imaging modalities anatomical regions. This design choice supports the generalizability of the proposed method across different scanners, clinical sites, and anatomical structures.
C. Gradient Dynamics and Conflict Resolution in Direct and Two-Stage Learning
C.1. Challenges in Direct Learning
Direct learning seeks to map Spest to Spe through a single neural network fairect. While the pixel-wise loss function (e.g. mean squared error (MSE)) is computed independently. the shared network parameters fdrecat create dependencies across all pixels during optimization. This parameter sharing leads to challenges in gradient dynamics, particularly in regions with high signal disparity. The optimization goal for direct learning is to minimize the reconstruction loss (e.g. MSE):
Liirect
Σ
[ (Spoa: Osieec))
Spre
(35)
N
The gradient of this loss with respect to the network parameters Odirect is given by:
A direct
Σ 2 Spre
Oz
(36)
00sireet
N
00
where z the model output. The term Spost depends nonlinearly on the contrast concentration [Gd] due the relaxation
mechanism in T1-weighted imaging:
T Tpost
(37)
+ |Gd]
This relationship amplifies the signal difference Spost Spre in regions with high [Gd], generating large gradient magnitudes. Conversely, non-enhanced regions ([Gd] = 0), the gradients are smaller and dominated by intrinsic tissue properties such as T and proton density p.
The disproportionate gradient contributions from contrast-enhanced regions cause bias in the parameter updates, which will leads to suboptimal performance, as the network prioritizes fitting high-contrast regions the expense of accuracy in non-enhanced regions, where smooth tissue-spedd -ssecispeccficc variations critical. This leads to gradient conflicts in the model training process. The gradient for single pixel is expressed as:
= 2. (z Spre).
(38)
Oz
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Submission and Formatting Instructions
In contrast-enhanced regions, the large signal differences caused by the nonlinear dependence [Gd] dominate the gradient:
post Spre ~ ([Gd))
(39)
whereas in non-enhanced regions, the gradient scales as:
Spoa
Spre ~ O(1).
(40)
This discrepancy is further exacerbated by the shared network parameters, the gradients from high-contrast regions propagate throughout the network, overshadowing updates for low-contrast areas. The result is gradient conflict that impedes accurate reconstruction of Pre-Contrast images.
C.2. Conflict Resolution via Two-Stage Learning
Two-stage learning resolves the gradient conflicts inherent in direct learning by decoupling the tasks of contrast detection and pre-contrast reconstruction. This framework consists of two sequentially optimized components, including a segmentation stage to localize contrast-enhanced regions, and a inpainting+ stage to synthesize the Pre-Contrast image using both the segmentation results and the Post-Contrast image.
Stage 1: Contrast Segmentation
The segmentation network fee learns binary map M, which identifies regions with significant contrast enhancement. its gradients with BCE loss constrained to binary classification, avoiding the variance amplification observed in direct learning. The gradient is:
d 0M
M 1, M 0.
M
(41)
1
Unlike the gradients in direct learning, which scale with the signal differences AS = Spost Spre. the segmentation gradients depend solely on classification errors and are bounded. This stability ensures that the network focuses on contrast detection without being dominated by regions with large intensity differences.
Stage 2: Pre-Contrast Reconstruction
The reconstruction network Jimpaint+ synthesizes the Pre-Contrase image Spee using both the Post-Contrast image Spea and the segmentation map M. The reconstruction loss is defined as:
Creoon
N Σ M (fimpiiot+ (Spost M; 0ccoon) - Spec)
By incorporating M. the reconstruction task focuses exclusively contrast-enhanced regions, while gradients for non- enhanced regions (M- = 0) are masked. For pixel in the enhanced region (M = 1), the gradient of the reconstruction loss
is:
ac @0ccon
Oz
N Σ M (z
Spre): D0
(42)
This formulation mitigates the gradient conflicts observed in direct learning. Unlike the direct approach, where the gradient magnitude is dominated by AS in high contrast regions, the two-stage framework ensures that reconstruction gradients are modulated by M, effectively isolating the tasks of contrast detection and Pre-Cone Contrast synthesis.
C.3. Experimental Results
To further analyze the learning behavior of direct learning methods (c.g., NestedUNet) and the proposed SPHERE framework. examine their loss curves during training. The L1 and SSIM loss curves in Fig. 10 indicate that direct learning methods tend to converge to suboptimal loss values, whereas SPHERE exhibits a continuous decline in loss, ultimately achieving superior performance.
Additionally, we assess the similarity between the loss curves of contrast and structural regions. To quantify this, we employ Pearson Correlation (Freedman et al., 2007), Cosine Similarity (Xia et al., 2015), and the Gradient Similarity Index (GSI). For contrast loss and structural loss I,, GSI is defined as:
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Submission and Formatting Instructions
L1 Loss
SSIM Loss
DIRECT
0.40
DIRECT
SPHERE
SPHERE
0.06
DIRECT.STD
0.35
DIRECT.STD
SPHERE.STD
SPHERE.STD
0.05
0.30
SSIM Loss
Loss
0.04
0.25
0.03
0.20
0.15
0.02
0.10
0.01
100
200
300
400
500
100
200
300
400
500
Training iterationsx20
Training Iterationsx20
Figure 10. The loss comparison between direct learning method and proposed SPHERE
2 2Σ VL. VL
GSI(Ie.))
(43)
Σ VIG +
and VI, di, where Vl. dl
dt represent their respective gradients. The term 2 2Σ Vle Vl, quantifies gradient alignment, while Σ VI de Σ VI? normalizes the score.
As shown in Tab. 6, the proposed SPHERE framework achieves significantly higher correlation and similarity in loss optimization between contrast and structural regions, demonstrating a more harmonized learning process. In contrast, direct learning exhibits lower similarity, suggesting potential optimization conflicts between contrast and structural components, as analyzed in Section. C.I.
Table Quantitative evaluation of the relationship between contrast and structural region losses, indicating the optimization consistency across different methods.
Method DIRECT
Pearson Correlation f
Cosine Similarity?
Gradient Similarity Index
0.5414
0.9210
0.1549
SPHERE
0.8226
0.9790
0.2638
D. Clinical Validation
To comprehensively assess the quality of the synthesized pre-contrast (Syn-Pre) images, invited two independent radiologists for evaluation. Reader #1 has over 15 years of clinical experience in radiology, and Reader #2 has 10 years. A total of 15 cases were reviewed, including a range of pathologies such as glioblastoma (GBM), lymphoma (CNS and Hodgkin's s-relateed), anaplastic astrocytoma, meningioma, oligodendroglioma,, Von Hippel-Lindau disease, and fungal/parasitic infections. Five evaluation criteria were used: Perceived Image Quality, Anatomical Alignment, Tissue Visualization (usability with Post-Contrass image), Diagnostic Value (when paired with Post-Contrast image), and Imaging Artifacts. Each metric was scored on 1-4 Likert scale.
Fig. 11 shows that Syn-Pre exhibits a highly similar and authentic pathological appearance compared SOC-Pre. Quantita- tively, Syn-Pre achieved higher scores than SOC-Pre in Perceived Image Quality (3.96 = 0.19 vs. 3.64 + 0.49), Anatomical Alignment (3.96 + 0.19 vs. 3.75 + 0.52), and Imaging Artifacts (4.00 + 0.00 vs. 3.89 + 0.31), indicating superior visual clarity, structural coherence, and reduced noise. While Tissue Visualization (3.68 + 0.43 vs. 3.86 + 0.30) and Diagnostic Value (3.68 + 0.55 vs. 3.86 = 0.36) scored slightly lower for Syn-Pre, the differences remain minimal and clinically acceptable. To further quantify this, one-sided Wilcoxon signed-ram tests were conducted under the null hypothesis that Syn-Pre underperforms SOC-Pre by 2 0.16 points. The resulting values were 0.01 59 for tissue structure and 0.0003 for
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Submission and Formatting Instructions
Post-Contrast
Syn-Pre
SOC-Pre
Post-Contrast
Syn-Pre
SOC-Pre
Meningioma
Anaplastic astrocytoms
Oligoastrocytomm
Turns
Tumor
hymphont
Figure 11. The example cases with various pathology types.
diagnostic value. Therefore, we reject this null hypothesis at the 0.05 significance level and confirm that Syn-Pre not meaningfully worse. Together, these reader study results, combined with the extensive evaluations, reinforce the strong performance and practical viability of Syn-Pre reliable substitute when SOC-Pre images unavailable or suboptimal.
E. Discussion
E.1. Assuming Binary Mask for Contrast Agent Concentration
In fact, assuming a uniform distribution of contrast agent uptake across specific organs simplifies the complex pharma- cokinetics of gadolinium-bass contrast agents. reality, contrast agent concentration varies spatially due to differences in vaseular permeability, perfusion rates, extracellular volume fractions, and clearance mechanisms across tissues. For instance, tumors with irregular angiogenesis accumulate contrast differently than healthy tissues, while highly perfused organs such the kidneys and liver experience rapid uptake and clearance. This variability means that global uptake mask M, derived solely from contrast enhancement, may fail to fully capture the true spatial heterogeneity of [Gd], leading to potential inaccuracies in estimating pre-contrast signal.
Luckily, although the inpainting+ process was designed for structural restoration, it inherently addresses this issue by integrating information from the Post-Contrast image. Since the Dost-Contrast image preserves both structural details and intensity variations related contrast agent distribution, provides richer context for reconstructing pre-contrast signals. The texture patterns in enhanced regions naturally encode information about local contrast concentration, vascular properties, and tissue heterogeneity, which proves useful in refining the pre-contrast estimation.
E.2. Base Model Investigation
This paper presents a novel physics-guided dual-stage learning framework for pre-contrast image synthesis. The proposed approach utilizes NestedUNet-brat based models for the autoencoder, segmentation, and inpainting+ processes. Despite employing relatively basic convolutional architecture, the proposed SPHERE framework outperforms advanced models such as Mamba and KAN in this setting. Future work will explore alternative model architectures within this framework to further enhance performance and generalizability.
E.3. Runtime Analysis
While the proposed model demonstrates reduced learning complexity compared to conventional approaches, it integrates three NestedUNet-baase components, which increases the overall inference time. To evaluate its computational efficiency in practical applications, we conducted a runtime analysis using two standard metrics: Throughput, measured in images per second (I/s), and Latency, measured in seconds per image (s/l).
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Submission and Formatting Instructions
Table 7. Runtime analysis comparing throughput and latency across methods.
Runtime Metrie
UNet
Au-UNNet
UNet++
SwinIR
UKAN
MambalR
BICEPS
SPHERE*
SPHERE (FP16)
Throughput (I/s)
1.12
1.06
0.97
1.04
1,10
1.33
1,06
0.45
0.59
Latency (s/I)
0.89
0.94
0.91
0.75
0.94
2.20
1.69
As shown in Tab. 7, the inference speed of the proposed SPHERE model is approximately 2x slower than existing baselines, primarily due to the added complexity of the dual-stage architecture. Nevertheless, from deployment standpoint, post-processing full DICOM series within or around five minutes is generally acceptable in clinical workflows. With FP16 precision, SPHERE processes approximately 177 slices under five minutes, meeting this practical constraint. If further speedup is needed, model simplification or hardware-level optimization could be considered.
E.4. Pre-to-Post Image Synthesis Feasibility
The equation in Eq. 11 can be naturally extended to the synthesis of post-contrast MRI from pre-contrast images. However, a critical challenge remains in accurately estimating the segmentation map, which is essential for distinguishing contrast- enhanced regions. The inherent variability in contrast uptake across different tissues and imaging protocols further complicates this task, making direct mapping approaches prone inconsistencies. Consequently, the current formulation does not fully address the complexities of pre-to-post contrast synthesis. While previous studies have investigated this problem, existing methods struggle to achieve clinically reliable results, often exhibiting artifacts insufficient contrast enhancement. A more robust approach is needed to improve the accuracy and generalizability of Pre-to-Poss -ost synthesis.
18


Reviews:
[{"review_id": "I3lN8WvnLF", "reviewer": "Reviewer_q8jE", "summary": "This paper proposes a novel staged, physics-grounded learning framework with a hyperintensity prior to synthesize Pre-Contrast images directly from Post-Contrast MRIs. The proposed method can generate high-quality Pre-Contrast images, thus, enabling comprehensive diagnostics while reducing the need for additional imaging sessions, costs, and patient risks. The authors claim it is the first Pre-Contrast synthesis model capable of generating images that may be interchangeably used with standard-of-care Pre-Contrast images. Extensive evaluations across multiple datasets, sites, anatomies, and downstream tasks demonstrate the model’s robustness and clinical applicability, positioning it as a valuable tool for contrast-enhanced MRI workflows.\n\n## Update after rebuttal: \n\nI appreciate the authors’ responses to my questions, especially involving experts to assess the quality of the synthesized pre-contrast images. I have updated my score accordingly.\n\nHowever, I'd like to point out that if you use a t-test to check the significance of the 'Reader Scores', you will find no significant differences between them, for example, 4.00 ± 0.00 vs. 3.89 ± 0.31. You might need to reformulate your words instead of claiming 'consistently outperform', which doesn't impact your conclusion, though.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for reviewing our manuscript from the clinical application perspective, your comments are truly constructive for us. We appreciate your recognition of our novelty, integration of domain knowledge, and potential clinical applicability. The motivation of our study is to provide a theoretically supported AI solution to address an unsolved application problem in MR imaging. Regarding the weakness, we provide the responses as below: (an External Link for Results Visualization: https://anonymous.4open.science/r/ICML25_rebuttal-63F3)    \n1.Thank you for raising this concern about clinical validation. We have invited two independent radiologists to comprehensively assess the quality of the synthesized pre-contrast images in comparison to the SOC pre-contrast images. Reader #1 has over 15 years of clinical experience in radiology, and Reader #2 has over 10 years. A total of 15 cases were reviewed. The pathologies included tumors, GBM (glioblastoma), lymphoma (CNS and Hodgkin’s-related), anaplastic astrocytoma, meningioma, oligoastrocytoma, Von Hippel-Lindau disease, and fungal/parasitic infection. Five metrics were used: Perceived Image Quality, Anatomical Alignment, Tissue Visualization (Usability with Post), Diagnostic Value (when +Post), and Imaging Artifacts. All metrics were scored using a 1–4 Likert scale. Please refer to Table 1 in the link for more metric details. The results from both readers are summarized as follows (see Fig. 1 and Fig. 2 in the link for additional statistical analysis and visualized results):  \nTab 2. Reader Scores\n| Metric                         | Syn-Pre Mean ± SD, | Syn-Pre Quartiles, | SOC-Pre Mean ± SD, | SOC-Pre Quartiles |\n|-------------------------------|-------------------|-------------------|-------------------|-------------------|\n| Perceived Image Quality       | 3.96 ± 0.19       | 4.00, 4.00        | 3.64 ± 0.49       | 3.00, 4.00        |\n| Anatomical alignment | 3.96 ± 0.19       | 4.00, 4.00        | 3.75 ± 0.52       | 4.00, 4.00        |\n| Tissure Visualization       | 3.68 ± 0.43       | 3.50, 4.00        | 3.86 ± 0.30       | 4.00, 4.00        |\n| Diagnosis Value   | 3.68 ± 0.55       | 3.00, 4.00        | 3.86 ± 0.36       | 4.00, 4.00        |\n| Imaging Artifacts             | 4.00 ± 0.00       | 4.00, 4.00        | 3.89 ± 0.31       | 4.00, 4.00        |\n  \nAs demonstrated by the results, the Syn-Pre images consistently perform better or comparable to SOC-Pre in several important aspects. Specifically, Syn-Pre achieved higher scores in perceived image quality (3.96 ± 0.19 vs. 3.64 ± 0.49), anatomical alignment with post-contrast (3.96 ± 0.19 vs. 3.75 ± 0.52), and imaging artifacts (4.00 ± 0.00 vs. 3.89 ± 0.31), suggesting superior visual clarity, structural coherence, and reduced noise. While visualization of tissue (3.68 ± 0.43 vs. 3.86 ± 0.30) and diagnostic value when paired with post-contrast (3.68 ± 0.55 vs. 3.86 ± 0.36) scored slightly lower for Syn-Pre, the difference remains minimal and clinically acceptable. Specifically, 12 out of 15 cases were rated equivalent to SOC-Pre in these two metrics, with only 3 cases showing slight degradation. To further quantify this, one-sided Wilcoxon signed-rank tests were conducted under the null hypothesis that Syn-Pre underperforms SOC-Pre by ≥0.16 points. The resulting P-values are 0.0159 for tissue structure and 0.0003 for diagnostic value. Therefore, we reject this null hypothesis and confirm that Syn-Pre is not meaningfully worse. Together, these reader study results together with the extensive evaluations reinforce the strong performance and the practical viability of Syn-Pre as a reliable substitute when SOC-Pre images are unavailable or suboptimal.\n\n2.For the common MRI sequences or modalities such as T1, T2, T2FLAIR, T2STAR, TOF, TRICKS, ADC, ASL, DWI, LOC, SSFP, and SWI, gadolinium-based contrast agents (GBCAs) are predominantly used in T1-weighted imaging, which serves as the clinical standard for contrast enhancement [1]. We acknowledge that contrast agents have limited but notable applications in other sequences such as T2-STIR, TOF, and SWI. The fundamental prerequisite for applying our method is the presence of hyperintense in the post-contrast images, which are not visible in the pre-contrast images. When this condition is met, our dual-stage learning framework which is driven by hyperintensity priors, can theoretically be extended to other sequences beyond T1. In future work, we plan to explore the generalizability of our approach to additional modalities.\n\n3.Please refer to Reviewer #2 item 1.   \nThank you again for taking time and efforts to review our paper, please feel free to raise a question if there is any confusion. Thank you!  \nReference\n[1] Lohrke, Jessica, et al. \"25 years of contrast-enhanced MRI: developments, current challenges and future perspectives.\" Advances in therapy 33 (2016): 1-28.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "Yes. The whole experimental sections.", "relation_to_broader_scientific_literature": "The paper can be used to deal with the real-world MRI generation problem.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "Strengths:\n\n1. The two-stage training paradigm (initial physics-based augmentation followed by deep-learning-based synthesis) seems innovative.\n2. The proposed model achieves better results (quantitatively and qualitatively) compared to prior work, indicating the success of integrating domain knowledge into the learning process.\n3. The proposed approach has the potential to reduce the need for multiple MRI scans while maintaining diagnostic quality.\n\nWeaknesses:\n\n1. It is unclear how well the generated synthetic pre-contrast images preserve pathology-related features in conditions like tumors, multiple sclerosis, or stroke. I am expecting to see more in-depth clinical validations as this paper focuses on real-world problems\n2. How can the proposed method be generalized to different MRI sequences and modalities?\n3. I am also wondering how each component of the proposed method benefic the performances. Could you please provide a more detailed ablation study to explicitly evaluate the impact of individual components?", "other_comments_or_suggestions": "N/A", "questions_for_authors": "N/A", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tLOpPWgLqn", "reviewer": "Reviewer_14Xf", "summary": "This paper proposes SPHERE, a staged and physics-grounded learning framework for synthesizing Pre-Contrast MRI images from Post-Contrast MRI scans. The key innovation lies in incorporating MRI physics principles and a hyperintensity prior into a two-stage deep learning model. The framework consists of segmentation and inpainting. Extensive experiments on multi-site MRI datasets demonstrate that SPHERE outperforms existing deep learning methods across multiple metrics and generalizes well to spine and breast MRI applications. The method also extends to artifact removal for corrupted Pre-Contrast images. The approach has potential clinical significance by reducing the need for additional imaging sessions, cost, and patient risk.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your meticulous and comprehensive review. We appreciate your recognition of our work on quantitative performance, mathematical support, prior knowledge incorporation, and model generalizability. Regarding the identified weaknesses, we provide the following responses:    \n1.Yes, the hyperintensity prior and two-stage framework are two critical components of our model, and quantifying their contribution to performance is important. We have added ablation studies on key components such as the Hyperintensity Prior, the Arbitrary Segmentation Branch, the Autoencoder module, the Dual Learning stage, and selection of τ.   \nTab 3. Ablation study on different modules and τ selection.  \n| Configuration               | PSNR ↑   | SSIM ↑  | CNR ↓   | LPIPS ↓ | GMSD ↓  | CFS ↑   | IRC ↑   | EIS ↑   |\n|----------------------------|---------|--------|--------|--------|--------|--------|--------|--------|\n| W/o Hyperintensity          | 35.7608 | 0.8842 | 0.0729 | 0.0434 | 0.0356 | 0.8970 | 0.8252 | 0.4041 |\n| W/o Abitrary Seg             | 36.3764 | 0.8951 | 0.0666 | 0.0346 | 0.0337 | 0.9068 | 0.8558 | 0.4703 |\n| W/o AE                    | 36.6764 | 0.9006 | 0.0635 | 0.0321 | 0.0328 | 0.9119 | 0.8585 | 0.5075 |\n| W/o Dual Step      | 34.5522 | 0.8580 | 0.0836 | 0.0479 | 0.0362 | 0.8462 | 0.8454 | 0.3746 |\n| SPHERE*           | 36.8244 | 0.9026 | 0.0628 | 0.0313   | 0.0315  | 0.9181 | 0.8684 | 0.5364 |\n| **τ selection** |   |\t|\t|\t|\t|\t|\t|\t|\n| τ = 0.06                   | 35.7835 | 0.8990 | 0.0651 | 0.0366 | 0.0320 | 0.9109 | 0.8560 | 0.5366 |\n| τ = 0.08                   | 36.8841 | 0.9034 | 0.0628 | 0.0298 | 0.0315 | 0.9179 | 0.8676 | 0.5319 |\n| τ = 0.10                   | 36.8244 | 0.9026 | 0.0628 | 0.0313 | 0.0315 | 0.9181 | 0.8684 | 0.5364 |\n| τ = 0.12                   | 36.8759 | 0.9035 | 0.0624 | 0.0299 | 0.0317 | 0.9176 | 0.8687 | 0.5333 |\n| τ = 0.14                   | 36.7256 | 0.9008 | 0.0635 | 0.0313 | 0.0320 | 0.9097 | 0.8702 | 0.5246 |\n  \nAbove quantitative and qualitative results in Fig. 4 on https://anonymous.4open.science/r/ICML25_rebuttal-63F3 shows that the key component such as Dual stage learning, Hyperintensity, and arbitrary seg are all beneficial to the model performances to different extents. For the τ selection, values in the range of 0.08–0.14 generally yield consistent performance with minimal variation. This suggests that our model is not highly sensitive to exact choice of τ, indicating robustness and fewer constraints on hyperparameter tuning. \n\n2.We actually do not intend to claim the computational efficency, Instead, we aim to highlight that the learning complexity or difficulty of the dual-stage learning method is lower than that of direct learning, as shown in Eq. 17. This does not necessarily imply faster model runtime. We apologize for any misunderstanding this may have caused. In terms of inference time, we added an runtime analysis per your request. Two metrics including throughput and latency are employed to measure the model runtime. Results are shown as below:   \nTab 4. Runtime Analysis  \n| Runtime Metric       | UNet | Att-UNet | UNet++ | SwinIR | UKAN | MambaIR | BICEPS | SPHERE* | SPHERE* (FP16) |\n|----------------------|------|----------|--------|--------|------|---------|--------|---------|----------------|\n| Throughput (I/s)     | 1.12 | 1.06     | 0.97   | 1.04   | 1.10 | 1.33    | 1.06   | 0.45    | 0.59           |\n| Latency (s/I)        | 0.89 | 0.94     | 1.03   | 0.96   | 0.91 | 0.75    | 0.94   | 2.20    | 1.69           |\n  \nAs shown in the table, the model speed of the proposed method is approximately 2× slower than other methods due to the dual-stage design. From an application perspective, we consider post-processing of a DICOM series within or ~ 5 minutes to be clinically viable. The current runtime of SPHERE (FP16) roughly meets this criterion (~177 slices in 5m). If further acceleration is needed on high resolution 3D scan, we can refer to TensorRT or Triton for faster inference on deployment. For training on a single A100 GPU, the time required for a direct learning model such as UNet++ is 2.02h, while SPHERE requires 6.10h due to its dual-stage optimization. We have also benchmarked the training time on different hardware platforms including V100, A100, and H100. Our latest setup enables training completion in 3.1 hours, significantly accelerating model development. Please refer to Fig. 5 in the external link for more details. So, we can conclude that our dual design may need more runtime for training/inference, but within the clinically acceptable range. Thank you for raising this valuable point. We will include it in the main text in a later revision.  \n   \n3. Please refer to Reviewer #1 item 1, thanks. \n\nThank you again for your careful review of our paper, your acknowledegement of our work is really inspiring to us, and we hope we addressed your concerns, if there is any other questions, feel free to let us know! Thank you!", "claims_and_evidence": "Claim 1: SPHERE synthesizes clinically viable Pre-Contrast MRI images from Post-Contrast scans.\nEvidence:\nThe method is tested on two large, real-world MRI datasets from multiple sites and scanners. It achieves higher PSNR, SSIM, and CNR compared to baseline models, supporting the claim of high-fidelity image synthesis.\n\nClaim 2: The two-stage learning framework improves synthesis quality over direct image-to-image translation.\nEvidence:\nThe paper provides a mathematical derivation of the complexity reduction and gradient stability benefits of the two-stage approach. Empirical results show that SPHERE outperforms state-of-the-art methods, which struggle with contrast preservation and structural accuracy.\n\nClaim 3:\nThe hyperintensity prior improves contrast segmentation and Pre-Contrast reconstruction.\nEvidence: The segmentation results demonstrate that incorporating a hyperintensity prior enhances contrast region detection. Comparative experiments indicate improved structural and contrast preservation.\n\nClaim 4: SPHERE generalizes to other medical imaging tasks.\nEvidence:\nThe model is fine-tuned on spine and breast MRI datasets, achieving strong quantitative results, demonstrating adaptability beyond brain MRI.\n\nWeaknesses in evidence:\nWeakness 1: The effectiveness of the hyperintensity prior is mentioned, but an explicit ablation study isolating its impact is missing.\nWeakness 2: While the results indicate strong performance, validation with radiologists or clinical usability studies would further substantiate the claim of clinical applicability.", "methods_and_evaluation_criteria": "The proposed MRI physics guided SPHERE framework is well-aligned with the problem of Pre-Contrast MRI synthesis. The two-stage learning approach, incorporating a hyperintensity prior, is a well-motivated methodological choice. The formulation effectively addresses the limitations of direct image-to-image translation by improving contrast segmentation and synthesis accuracy.\nThe evaluation criteria are appropriate for assessing image synthesis quality. The authors use standard image quality metrics, including PSNR, SSIM, CNR, and LPIPS, which are widely accepted for medical image analysis. The inclusion of multi-site, multi-scanner datasets enhances the robustness and generalizability of the findings. Additionally, downstream tasks (e.g., low-dose contrast simulation, spine and breast MRI applications) provide further validation of clinical utility.", "theoretical_claims": "Yes", "experimental_designs_or_analyses": "Yes", "relation_to_broader_scientific_literature": "This paper builds on existing work in medical image synthesis, MRI reconstruction, and physics-informed deep learning while introducing a novel two-stage, physics-grounded approach for Pre-Contrast MRI synthesis.\n\nMedical image synthesis:\nPrior works, such as UNet-based image-to-image translation and transformer-based synthesis models, have been applied to MRI reconstruction but often fail to preserve contrast details when synthesizing missing sequences.\nThe proposed SPHERE framework extends these efforts by explicitly modeling MRI physics to improve synthesis quality.\n\nPhysics-Guided deep learning in MRI:\nThe paper aligns with trends in physics-informed learning. Unlike purely data-driven approaches, SPHERE incorporates MRI signal equations to constrain the learning process, similar to prior work in quantitative MRI reconstruction.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths\n1. The paper presents a novel two-stage physics-grounded approach for Pre-Contrast MRI synthesis, integrating MRI signal modeling with deep learning, which is an innovative contribution beyond purely data-driven synthesis methods.\n\n2. The method addresses a practical problem in medical imaging, reducing the need for additional scans, which could lead to cost savings and reduced patient risk. The evaluation on real-world multi-site datasets enhances its potential clinical impact.\n\n3. The experiments are rigorous and diverse, including:\nComparisons with strong baselines (UNet, SwinIR, UKAN).\nMultiple quantitative metrics (PSNR, SSIM, CNR, LPIPS).\nDownstream clinical applications (spine, breast MRI, and low-dose contrast simulation).\n\n4. The paper is generally well-structured with detailed methodological explanations.\n\nWeaknesses\n1. While the paper presents intuitive justifications for the hyperintensity prior and two-stage framework, an explicit ablation study quantifying their contributions is missing.\n\n2. The two-stage design is claimed to be computationally more efficient, but there are no runtime comparisons or training time analyses to support this claim.\n\n3. While the method performs well quantitatively, there is no validation by radiologists to confirm the clinical realism and usability of the synthesized Pre-Contrast images.", "other_comments_or_suggestions": "No", "questions_for_authors": "No", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "n5yGxDDKcf", "reviewer": "Reviewer_YXmq", "summary": "This work discusses a deep learning method for recovering pre-contrasted MRI from post-contrasted MRI. The authors propose to first estimate a thresholded map as a mask indicating contrast agent update. This mask is then fed as an additional conditioning signal for recovering the pre-contrast image. The authors also discussed an artifact removal approach for enhancing pre-contrast images. The proposed framework is evaluated against several other types of basic feed forward neural network architectures.\n\n## update after rebuttal\n\nI would like to thank the authors for the efforts especially for the additional comparisons and clarifications. \n\nWith that being said, I still find the manuscript suffers somehow from unjustified claims / design choices and flaws in writing structures that are very unlikely to be addressed in a revision (and it may not be of the best practice to first introducing two heavy components: AE and a complicated artefact removal framework which had led to quite a lot confusions and then suddenly claiming they are not essential or are just for extension purpose). Also, the huge amount of hyper-parameters (as pointed out by Reviewer `pkvY`) render the proposed framework very difficult to be applied to other datasets by readers. I would therefore keep my current rating.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your in-depth review of our manuscript. Your comments are constructive and will help improve the quality of our work. In this manuscript, we propose a novel MRI theory-driven method to address a challenging problem in MRI imaging. Please find our detailed responses to your comments below: \n\nClaim:  \n1.(Comparison to other methods such as {1-6}): Thank you for raising this point. Per your suggestion, we conducted three additional comparative experiments using models No. 2, 3, and 6 from your recommended list. For No. 3 and 6, we adapted them to the same pipeline used by SPHERE. For the Syn-Diff model (No. 2), we trained it for 40 epochs, which took approximately 80 hours on two A100 GPUs. The quantitative results are summarized as follows:     \nTab 5. Additional Comparasions    \n| Models | PSNR ↑   | SSIM ↑  | CNR ↓   | LPIPS ↓ | GMSD ↓  | CFS ↑   | IRC ↑   | EIS ↑   |\n|------------------|---------|--------|--------|--------|--------|--------|--------|--------|\n| DuDoDR-Net     | 32.6218 | 0.7974 | 0.1078 | 0.0738 | 0.0404 | 0.6854 | 0.8143 | 0.2222 |\n| Dose Reduction | 34.8808 | 0.8665 | 0.0804 | 0.0492 | 0.0358 | 0.8450 | 0.7847 | 0.3941 |\n| Syn-Diff\t            | 35.7180 | 0.8961 | 0.0728 | 0.0337 | 0.0325 | 0.7068 | 0.8633 | 0.5434 |\n| SPHERE*           | 36.8244 | 0.9026 | 0.0628 | 0.0313 | 0.0315 | 0.9181 | 0.8684 | 0.5364 |\n  \nPlease also refer to Fig 3. in https://anonymous.4open.science/r/ICML25_rebuttal-63F3 for qualitative evaluation. DuDoDR-NET and Dose Reduction perform significantly worse, while Syn-Diff indicates somewhat closer results. However, it overemphasizes background regions and fails on pathological structures. These outcomes further support our claim that existing models struggle to balance structural fidelity and contrast enhancement. In contrast, our model provides the most effective solution to this challenging task.    \n2.(Line 058 right): We totally agree with you on this, Sorry for this mistake.  \n3.(M is still a function of S_{post}), we will add one more equation of M in terms of S_{post} to make it clearer.   \n4.(Line 195 left): Yes, the output of the arbitrary segmentation model is combined with the Hyperintensity branch to make a fused prediction, the loss function is applied on the fused prediction for training. We will refine the wording in revision.  \n5.(Unclear how Eq. 16 is reached): Yes, as noted, our task inherently involves a sequential combination of segmentation and inpainting+ subtasks. With our dual stage learning, the complexity is additive with modular training [1]. However, directly modeling these together with a single network needs to encode all segmentation-to-inpainting mappings simultaneously. This multiplicative complexity arises naturally from the fact that the model needs encode every possible combination of segmentation-to-inpainting mappings. We will explicitly clarify this rationale in our revision.  \n6.[Evaluation in-house datasets] In this study, we tried our best to evaluate our model more extensively like across multiple datasets, sites, anatomies, and downstream tasks. But I am sorry we cannot disclose datasets due to license constrait. In future, we plan to apply our model to public datasets to further support reproducibility.  \n\nWeakness:  \n1,2. The autoencoder is a marginal component of our model. It works with a scaling factor to adjust image intensity, which mgiht also be handled by raw input. We keep it to subtly suppress non-structural noise, making hyperintensity extraction more robust. Though not explicitly designed for denoising, the AE learns compressed bottleneck representations that capture structural and semantic manifold, naturally reducing inconsistent noise or redundancy [2]. We apologize for missing this rationale and will include it in the next revision. An ablation study on the AE is also provided in Fig 4. in Link for details. Overall, we find AE marginally beneficial.  \n3.Please refer to Reviewer #4 Item 4.  \n4.The artifact removal component is included to extend our model’s applicability to scenarios with corrupted images. The current implementation serves as a proof of concept, and we plan to explore it further in future work.  \n\nThank you again for taking the time to rigorously review our paper! Your comments will undoubtedly enhance the overall quality of our work like on the model rationale. We sincerely appreciate your thoughtful feedback. Please feel free to reach out if you have any further questions.  \n\nReference  \n[1] Leung, K. H., et al (2020). A physics-guided modular deep-learning based automated framework for tumor segmentation in PET. Physics in Medicine & Biology, 65(24), 245032.  \n[2] Bartlett, O. J., et. al (2023). Noise reduction in single-shot images using an auto-encoder. The Royal Astronomical Society, 521(4), 6318-6329.", "claims_and_evidence": "Claim: Line 095 left: The proposed work \"present a significant advancement in MRI image by developing a method capable of generating high-quality pre-contrast images\"\nFact check: This claim cannot be substantiated unless being compared with commonly used medical image translation / quality enhancement methods such as [1-6]. Given the similar mathematical formulation (pixel to pixel mapping), even some of them are originally designed for slightly different purpose, re-purposing them to the pre-contrast recovery should be straightforward.\n\nClaim: Line 058 right: The proposed methods are extensively evaluated on two real-world datasets we collected from two hospitals, demonstrating their robustness.\nFact check: Robustness are normally characterized by stable performance against OOD data or adversarial samples at test time. Unlikely to be the case described in the Experiment section.\n\nClaim: Training a simple image-to-image synthesis network to map Post-Contrast to Pre-Contrast images often fails to balance the synthesis of the structural and contrast information in the image.\nFact check: Line 158 left: M is still a function of S_{post} though.\n\nClaim: Line 195 left: \"...a conventional deep segmentation model to guarantee model precision and robustness ...\"\nFact check: convolutional segmentation models alone cannot guarantee model precision and robustness without proper training data / training approach.\n\nClaim: Eq. 16 The proposed method reduced the complexity from multiplicative to additive.\nFact check: It is unclear how Eq. 16 is reached given the sequential nature of Eq. 11 and 12.\n\nClaim Line 265 right: \"these methods represent the golden standard approaches in image enhancement, segmentation, and synthesis.\"\nFact check: No evidence. E.g. for image enhancement and synthesis there exists much more advanced methods such as [1-6].\n\n1. Adaptive latent diffusion model for 3d medical image to image translation: Multi-modal magnetic resonance imaging study\n2. Unsupervised Medical Image Translation With Adversarial Diffusion Models\n3. DuDoDR-Net: Dual-domain data consistent recurrent network for simultaneous sparse view and metal artifact reduction in computed tomography\n4. Target-guided diffusion models for unpaired cross-modality medical image translation\n5. Cascaded multi-path shortcut diffusion model for medical image translation\n6. A generic deep learning model for reduced gadolinium dose in contrast‐enhanced brain MRI", "methods_and_evaluation_criteria": "The evaluation metrics are relevant. However, given that most experiments are performed on two in-house datasets, the reproducibility of the proposed work is unclear.", "theoretical_claims": "The proposed work is mostly empirical. Please find my additional comments in `Claims And Evidence` section.", "experimental_designs_or_analyses": "The claimed superiority cannot be substantiated without systematic comparisons with recent medical image enhancement / modality translation / artifact removal works, such as  [1-6]. Given the similar mathematical formulation (pixel to pixel mapping), even some of them are originally designed for slightly different purposes, applying them to pre-contrast recovery should be straightforward.", "relation_to_broader_scientific_literature": "This work falls into the categories of medical image quality enhancement / modality translation / artifact removal, given the similar mathematical formulations.", "essential_references_not_discussed": "Works on medical image enhancement / modality translation / artifact removal, such as  [1-6] should be discussed, given the similar mathematical formulations (learning pixel to pixel mappings in image intensity domain).", "other_strengths_and_weaknesses": "Strengths:\n- The authors have presented the mathematical model for image contrast enhancement.\n- Improved performances are shown compared with experimented neural networks.\n\nWeaknesses:\n- The paper suffer from a lack of rationale for many design choices: E.g., Why do the authors process S_{post} with an autoencoder?\nSec. 2.3 can be distracting as it is not closely centered at the pre-contrast recovery problem.\n- The motivation for processing S_{post} with AE is unclear.\n- The threshold \\tau is subject to manual choice and it is critical for defining M_{true}. Given the heterogeneity in real-world MRI acquisition and its non-quantitative nature choosing a proper \\tau can be difficult in real world.\n- Artifact removal: It is related but not centered on the pre-contrast recovery. It should instead be put as a standalone work and carefully assessed alone. Also, little information about the rationale behind and the methodology is presented in the main text.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "Given that most experiments are performed on two in-house datasets, how would the reproducibility of the proposed work be assessed?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {"ethical_review_concerns": "N/A, given the claims in line 236-237 right."}}, {"review_id": "mDd0xIApus", "reviewer": "Reviewer_pkvY", "summary": "This paper is about using post-contrast MRI to create pre-contrast MRI via deep learning. Physics principles are built into the model. To tackle the complexity in setting up the model and its training, a two-stage approach is presented, which alleviates the challenge in handling the complexity. The approach is set up as an inpainting process that first learns about a mask in post-contrast MRI and then rebuilds the pre-contrast MRI.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for taking time and efforts to review our paper, your opinon is really appreciated. Thank you for acknowledging our work’s theoretical contribution, motivation and usage of the physcis principles. The goal of this project is to leverage the power of AI4Science to tackle unsolved challenges in MRI applications, which we believe is as equally important to achieving a higher score on well-studied tasks. For each weakness item, our response is listed as below.  \n\n1.The left is derivative, the right is partial derivative, which is minorly different.  \n2.Yes, we agree that ‘prior’ generally refers to information known beforehand, but it does not necessarily imply a temporal sequence in MRI scans. A more precise definition is: prior knowledge refers to any information about the problem beyond the training data. In our study, the prior is the assumption that contrast uptake regions typically appear hyperintense compared to non-enhanced areas [Line 201]. Equations 19–20 are designed to enforce this prior in a differential manner. The prior is preset for all training images. \n3.Eq 22 defines the psudo ground truth for Stage 1, there is no regularization on it. But for the output of stage 1, we use regularization to ensure the model effectively learns the true hyperintensity prior like in [1]. The regularizer is assigned a low learning rate to avoid ruining the overall latent learning process.   \n4.The initial selection of τ is 0.1. This subtraction imaging technique, $\\mathbf{S}{\\text{post}} - \\mathbf{S}{\\text{pre}}$, is widely used in clinical practice [2] to capture contrast enhancement, with τ applied just to suppress background noise. Although τ is chosen empirically, its practical range is narrow (e.g., 0.08–0.12). A simple grid search on a few representative cases (e.g., τ ∈ [0.08, 0.10, 0.12]) is typically sufficient. We also explored different τ values in the ablation study (Reviewer 2, Item 1).        \n5.You are right! basically, the proposed model is trained to mimic Eq. 11. In our work, we disentangle the whole learning process to two stage learning. Different losses are designed to facilitate end-to-end model training. Similar to item 3, a light regularization term is applied to constraint the model to adapt to the physcis law.  \n6.Please refer to Item 3.   \n7.Thank you for raising this important question regarding the applicability of our model given the presence of nine weighting parameters (from Eq. 31 and 34). We offer two practical solutions:  \n(1) Use of Predefined Weights:\nThese weights were set based on the intrinsic properties of each loss function, not on specific data modalities or anatomies, and have yielded satisfactory results across scanners, sites, and anatomical regions. Below is the rationale for each:  \n* $\\lambda_{\\text{L1}} = 1$: Standard for pixel-wise accuracy.  \n* $\\lambda_{\\text{SSIM}} = 10$: SSIM ranges [0, 1], so we boost its contribution.\n* $\\lambda_{\\text{perceptual}} = 0.5$: Operates on high-dimensional feature space, typically yielding larger values; thus, we scale it down. \n* $\\lambda_{\\text{adv}} = 1$: Realism is equally important to pixel similarity.\n* $\\lambda_{\\text{Inpaint+}} = 1$: We treat segmentation and inpainting as equally critical.\n* $\\lambda_{\\text{ae}} = 1$: Autoencoder output should match L1-level fidelity.\n* $\\lambda_{\\text{bce}} = 10$: BCE loss yields small values over binary masks; we scale it up for balance. \n* $\\lambda_{\\text{hyper}} = 0.1$: Physics prior should guide but not dominate learning.\n* $\\lambda_{\\text{psyn}} = 0.01$: Regularization terms are generally weighted lower to avoid over-constraining.  \n(2) Use of Normalized Loss Weighting:  \nAlternatively, we can apply a simple approach by setting​$\\lambda_{i}  = \\frac{1}{\\mathcal{L}_i}$ for each loss term $\\mathcal{L}_i$, allowing all objectives to converge uniformly.  \nThese options support the generalizability and practical utility of our method without the need for extensive manual tuning.  \n8.While each stage has its own loss function, the model is trained end-to-end, similar to multi-task learning [3]. We apologize for the confusion and will clarify the separation of stage and final losses in future revisions.   \n\nThank you again for your detailed and extensive comments, we are sorry our current manuscript might cause some confusion and misunderstanding, Hope our response can address the confusions. In later revision, we will update our manscript to make it clearer according to your comments.  Feel free to let us know if there is any questions. Thank you!  \n\nReference:  \n[1] Myronenko, Andriy. \"3D MRI brain tumor segmentation using autoencoder regularization.\" Springer International Publishing, 2018.  \n[2] Hubbard, C., et al. The use of MRI digital subtraction technique in the diagnosis of traumatic pancreatic injury. Radiology Case Reports, 14(5), 639-645.  \n[3] Zhang, Y., & Yang, Q. (2018). An overview of multi-task learning. National Science Review, 5(1), 30-43.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Yes", "experimental_designs_or_analyses": "Yes", "relation_to_broader_scientific_literature": "The paper is well related to the broader scientific literature and presents a method for reconstructing a missing modality in MRI.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "The strength can be found in two aspects. One is to construct pre-contrast MRI from post-contrast MRI, which is not well covered in existing research. The other is the inclusion of physics-based principles into the reconstruction model, but please see comments below.\n\nWeaknesses are\n1. Why dS_pre/dS_post appeared on both sides of Eq. (15)? \n2. It is not clear how Eq. (19-20) derive the brightness prior H. By prior, it generally means the information known beforehand, for example, before MRI is acquired. But from Eq. (19-20), it seems the prior is derived from post-contrast MRI via auto-encoder and softmax, in this sense, it is unclear if that qualifies as prior information, unless I am missing something here.  \nFurthermore, is the prior H calculated slice-by-slice for a post-contrast MRI, or is it calculated only once for the whole post-contrast MRI series? \n3. Why is there a need to use a regularization term in Eq. (22)? \n4. How is \\tau determined in Eq. (22)?\n5. It is not clear how the deep learner in Stage 2 works or gets trained? Does it somehow incorporate the form of Eq. (11) in the deep learning model? Or is it just a deep learning model trying to mimic Eq. (11)?\n6. How is the regularization term, Eq. (23), used in the loss function of Stage 1? This should be given in the main text instead of the appendix.\n7. The practical applicability is a concern, as there are large number of weight parameters to tune, as given in Eq. (31) and (34). These many weight parameters may pose a difficult for users to select a good combination. \n8. The relationship between Eq. (34) and Eq. (31) is confusing. It seems Eq. (34) includes the loss term given in Eq. (31), the inpainting+ loss, but according to the main text, an advantage of the paper is to separately train the masking step and inpainting step, then why does Eq. (34) involve Eq. (31)?", "other_comments_or_suggestions": "Please refer to Strengths and Weaknesses.", "questions_for_authors": "Please refer to Strengths and Weaknesses.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This manuscript presents SPHERE, a staged physics-grounded learning framework for synthesizing pre-contrast MRI from post-contrast scans. The approach integrates MRI physics principles and a hyperintensity prior into a two-stage deep learning model comprising segmentation and inpainting steps. The reviewers acknowledged the paper's novelty in addressing an important clinical challenge and its thorough theoretical foundation. After rebuttal, the authors provided extensive additional experiments including reader studies with radiologists, ablation analyses, and comparisons with recent methods, which strengthened the empirical validation. The clinical reader study demonstrated that synthetic pre-contrast images achieved comparable or superior scores to standard-of-care images across multiple quality metrics. However, some reviewers remained concerned about aspects of the methodology, particularly the large number of hyperparameters and clarity of certain design choices. While the authors clarified that the autoencoder and artifact removal components were optional extensions rather than core elements, there were differing views on whether the manuscript structure effectively conveyed this. The reviewers' scores showed limited convergence after rebuttal, with two maintaining weak accept recommendations and two keeping weak reject positions, primarily due to presentation rather than fundamental technical issues. The extensive experimental validation and clinical relevance were viewed positively, though opportunities remain to improve the clarity of the methodological exposition.
Decision: Accept (poster)