Ordered-subsets Multi-diffusion Model for Sparse-view CT Reconstruction

Bin Huang; Minghui Zhang; Pengfei Yu; Qiegen Liu; Shaoyu Wang; Weiwen Wu

REVIEW 4 major objections 4 minor 32 references

Ordered-subsets Multi-diffusion Model for Sparse-view CT Reconstruction

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper claims that splitting CT projection data into ordered subsets, training a diffusion model on each subset, and refining with a whole-sinogram diffusion model reconstructs sparse-view CT images with higher PSNR/SSIM than…

desk verdict OSMM is a plausible new combination of per-subset diffusion models plus a whole-sinogram diffusion model for sparse-view CT; the empirical claim is likely true, but the paper under-reports uncertainty and contains a concrete table error. read the letter →

arxiv 2505.09985 v1 pith:EHHFUHIP submitted 2025-05-15 eess.IV cs.CV

Pengfei Yu , Bin Huang , Minghui Zhang , Weiwen Wu , Shaoyu Wang , Qiegen Liu This is my paper · ORCID

classification eess.IVcs.CV

keywords sparse-viewCTscore-baseddiffusionmodelorderedsubsetssinogramreconstructionunsupervisedlearningimagegenerativepriordataconsistency

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes OSMM, a two-stage diffusion-model pipeline for sparse-view CT reconstruction. Instead of feeding the full sinogram to one score-based diffusion model, it splits the projection views into ordered subsets, trains a separate diffusion model on each subset (MSDM), and then uses a whole-sinogram diffusion model (OWDM) as a global consistency constraint. The authors claim this reduces the difficulty of learning the projection data distribution, preserves fine details, and corrects errors, leading to better reconstruction quality. Experiments on AAPM, CIRS phantom, and preclinical mouse data report that OSMM beats FBP, U-Net, FBPConvNet, patch-based DDPM, and GMSD in PSNR/SSIM across 50–180 views. If correct, the method offers an unsupervised, sparsity-adaptive alternative to supervised and single-model generative approaches.

What carries the argument

The operative mechanism is the ordered-subsets division of the sinogram: projection views $1,\dots,M$ are partitioned into $N$ disjoint subsets in round-robin order, with view $n$ assigned to subset $n$. Each subset is then handled by an independent variance-exploding SDE score model. The MSDM stage applies the $N$ subset predictors with per-step data consistency; the OWDM stage merges the refined subsets and runs one whole-sinogram predictor, again with data consistency. This alternating scheme carries the argument by decomposing the learning task.

What would settle it

A controlled experiment that matches total compute: train a single whole-sinogram diffusion model with the same architecture, parameter count, and total training steps or GPU time as the N subset models together. If the single model matches or exceeds OSMM's PSNR/SSIM on the same sparse-view test data, the claimed benefit of subset division is not real. Also, training OSMM with N=1 inside the same code should reproduce OWDM-only performance; any gap must then be attributed to subset learning.

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Extended reading notes

Core claim

OSMM's core discovery is that ordered-subsets partitioning of the projection data turns one hard diffusion-learning problem into several easier ones: each subset diffusion model (MSDM) reconstructs its own sparse sinogram, recovering fine details, while the one-whole diffusion model (OWDM) keeps the merged sinogram globally consistent. Iterating the two stages with data-consistency updates produces sinograms that, after filtered back projection, have higher PSNR and SSIM than those from FBP, U-Net, FBPConvNet, patch-based DDPM, and GMSD. The authors further claim that the unsupervised training on full-view sinograms transfers across datasets and sparsity levels.

Load-bearing premise

The load-bearing premise is that splitting the projection data into ordered subsets genuinely lowers each diffusion model's learning difficulty while preserving the information needed for fine details; the paper gives this as a heuristic with no statistical or convergence analysis.

Editorial extensions

If this is right

Sparse-view CT reconstructions from as few as 50–60 views can reach PSNR values above 37 dB on AAPM data, roughly 3 dB higher than the next best generative baseline.
The method transfers across scanners and anatomies: models trained only on AAPM data improve CIRS phantom and preclinical mouse reconstructions without retraining.
At higher view counts (120, 180, 100) OSMM still gains, implying the subset prior remains useful even when the inverse problem is less ill-posed.
Ablation shows both stages matter: removing either MSDM or OWDM lowers PSNR, so the two-stage alternation is a genuine part of the improvement.
Increasing the number of subsets from 2 to 3 does not consistently improve results, suggesting there is an optimal split count.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If subset division is the real driver, the same ordered-subsets trick could be applied to other domains with large, redundant measurement spaces, such as MRI k-space or PET sinograms, where per-partition score models might ease training.
The paper's 'reduced learning difficulty' rationale predicts that the gain over a single model should grow with the redundancy of the full sinogram; a testable extension is to vary the amount of angular overlap in the projection data and measure the PSNR gain.
Because the alternating MSDM/OWDM scheme lacks a convergence guarantee, a practical extension would be to analyze it as a fixed-point iteration or replace the Predictor with a predictor-corrector sampler to see whether the data-consistency steps actually contract.
The subset-count effect (N=2 vs N=3) hints at a bias–variance trade-off: more subsets lower per-model difficulty but increase the chance of inconsistent merges; finding the automatic rule for N would turn the heuristic into an algorithm.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing here is the architecture: instead of training one diffusion model on the full sinogram, the authors split projection views into ordered subsets round-robin style (borrowed from OSEM), train a separate score model on each subset, and then run an alternating scheme that also consults a whole-sinogram diffusion model, with data consistency steps in between. That specific two-stage combination is not in the cited literature, and the paper shows it works on three datasets, including generalization from AAPM training to CIRS phantom and preclinical mouse data. The ablations in Table IV are useful because they show both the subset models and the global model contribute. The code is public. That is real value for a medical imaging audience.

The soft spots are recognisable. Tables I-III report single means, no standard deviations, no repetition count, no significance tests, so the superiority claim is narrower than the abstract suggests. Table II has an actual inconsistency: for the CIRS 180-view case, OSMM is listed as PSNR=46.87 dB and MSE=0.21e-3; those numbers do not match for normalized data (the MSE should be about ten times smaller). The abstract also claims noise resilience, but no noisy-projection experiment is reported. The motivation in Section III-A, that subset splitting reduces learning difficulty, is heuristic and not supported by any formal argument; the alternating algorithm in Algorithm 1 has no convergence analysis. None of these are fatal, but they need to be addressed before the performance claim is fully trustworthy.

I want to be clear about what holds up. The math is standard score-based SDE theory correctly applied. The method is plausible and internally coherent, and the empirical pattern is consistent across all three datasets. The table typo is probably a transcription error rather than a sign of fabricated numbers, but it needs fixing. The citation pattern looks fine: the paper builds on the authors' own GMSD work and on OSEM, and it compares against external baselines.

This paper deserves a serious referee. The idea is useful, the experiments are reasonably broad, and the flaws are reporting problems plus missing uncertainty quantification, not a load-bearing logical break. My recommendation: send it to peer review, ask the authors to correct the table, add error bars or at least multiple runs, run at least one noisy-projection experiment to back the noise-resilience claim, and tone down the abstract until the evidence is there.

Referee Report

4 major / 4 minor

Summary. The paper proposes OSMM, an unsupervised ordered-subsets multi-diffusion model for sparse-view CT reconstruction. The method divides full-view sinogram data into multiple view subsets, trains a separate score-based diffusion model (MSDM) on each subset, and then applies a whole-sinogram diffusion model (OWDM) as a global consistency constraint, with alternating data-consistency updates during iterative reconstruction. Experiments on AAPM challenge data, a CIRS phantom, and preclinical mouse data compare OSMM against FBP, U-Net, FBPConvNet, patch-based DDPM, and GMSD, reporting that OSMM achieves the best PSNR/SSIM/MSE at all tested view counts. Ablation studies examine the contributions of MSDM and OWDM and the effect of the number of subsets.

Significance. If the reported empirical results hold, OSMM would provide a generally applicable unsupervised sinogram-domain prior for sparse-view CT that improves on single-model diffusion baselines, with generalization demonstrated across a human-CT test set, a phantom, and a preclinical mouse dataset. The paper has several strengths: the evaluation is on held-out data not used in training, the method is compared against established baselines rather than only against the authors' prior work, ablations isolate the contribution of each stage, and the source code is publicly linked. These strengths make the central claim worthy of serious consideration, and the paper could be a useful contribution to the diffusion-based CT reconstruction literature. However, the significance is currently limited by the lack of statistical reproducibility evidence and by an internal inconsistency in the reporting of one of the headline quantitative results.

major comments (4)

[§IV-C, Tables I–III] The central claim that OSMM 'outperforms' all baselines at every view count rests on single-run point estimates with no standard deviations, no number of repeated experiments, and no significance tests. At the highest view counts the margins over GMSD are small (e.g., Table I: 43.69 vs 41.44; Table II: 46.87 vs 42.86; Table III: 40.20 vs 39.07), so without variance information the superiority claim is not statistically supported. Please report means and standard deviations over at least three independent runs, or otherwise provide a significance analysis.
[§IV-C, Table II, CIRS 180-view row] The CIRS 180-view entry reports PSNR=46.87 dB and MSE=0.21e-3. For normalized images these two quantities are mutually inconsistent: PSNR=46.87 dB corresponds to MSE≈0.021e-3, while MSE=0.21e-3 corresponds to PSNR≈36.8 dB. This internal inconsistency indicates a reporting or computation error in a central results table and must be corrected and verified before the generalization claim can be accepted.
[Abstract and §V] The abstract claims that OSMM outperforms traditional diffusion models in 'noise resilience,' but no experiment with noisy projections is reported anywhere in the paper. The only mention of noisy data is a qualitative statement in §V that 'when projection data is noisy, using too many subsets can hinder convergence.' Either add explicit experiments with noisy sinograms to support the noise-resilience claim, or remove that claim from the abstract.
[§III-A and Algorithm 1] The method's rationale rests on the heuristic that 'dividing the projection data into multi-subsets can more effectively represent prior information' and that per-subset diffusion reduces learning difficulty. This premise is not justified theoretically or empirically, and Algorithm 1's alternating MSDM/OWDM scheme is presented without a convergence analysis or a clear objective that the iterations are guaranteed to minimize. Since the paper's contribution is precisely this decomposition, please add either a formal convergence argument for the alternating scheme or an empirical study (e.g., reconstruction error vs. iteration number, and a comparison of per-subset versus whole-data learning curves) that supports the stated motivation.

minor comments (4)

[§IV-C, Fig. 10 caption] The caption refers to 'GSDM' while the text and tables use 'GMSD'; please harmonize the naming.
[§IV-A] The AAPM data description states that 'the FBP algorithm was employed to obtain artifact-free images at 720 projection angles, serving as the standard reference,' but it is unclear whether the 720-view FBP reconstruction is truly artifact-free; please clarify the reference standard and its relation to the original high-dose CT images.
[§II-C] The subset definitions in the text (e.g., x1 = {1, N+1, 2×N+1, ..., (N−1)×N+1}) appear to contain off-by-one inconsistencies; for N subsets and M views, the last element in x1 should be M−N+1 rather than (N−1)×N+1 when M is a multiple of N. Please fix the notation.
[§IV-C, Table I] The statement in the text that 'Analysis of 90 views reconstructions reveals a similar trend to that observed with 90 views' appears to contain a typo; the second '90 views' should likely be '60 views' or another view count.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: OSMM's improvement claim is empirical and tested on held-out data; the subset-diffusion construction is a new architecture, not a renamed fit.

full rationale

I found no circular step. The derivation chain is self-contained: Eq. (3) is a standard regularized inverse-problem formulation, Eqs. (10)-(14) are the standard VE-SDE score-matching objectives applied to each subset, and the iterative scheme in Eqs. (15)-(21) and Algorithm 1 alternates diffusion-prior refinement with data consistency. The central claim that OSMM outperforms single-model diffusion baselines is supported by quantitative comparisons on held-out AAPM test slices and on CIRS phantom and preclinical mouse data not used in training; no fitted parameter is later renamed as a prediction, and no quantity reported as a prediction is equivalent by construction to a training target. The motivating statement in Section III-A that subset division 'can more effectively represent prior information' is a heuristic rather than a proven theorem, but an unsupported heuristic is not circularity. The only self-referential element is the authors' earlier GMSD model [14] being used as a comparison baseline, but the paper's conclusion does not depend on GMSD being correct; OSMM is evaluated against it as an external competitor. The Table II PSNR/MSE inconsistency and the unsupported 'noise resilience' wording are correctness and evidence concerns, not examples of circular derivation.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced; the MSDM and OWDM are algorithmic components, not entities with independent falsifiable handles. The main free parameters are architectural and training hyperparameters, several of which are not reported.

free parameters (4)

number of subsets N = 2 (3 in comparison)
Views are divided into N subsets (round-robin); N=2 is used for main experiments, N=3 tested in Table V; no principled selection rule given.
regularization weights r1, r2
Weights balancing data fidelity and MSDM/OWDM regularization in Eq. (15); values not specified in paper.
subset regularization factors lambda_n and lambda
Weights in Eqs. (16) and (20) for per-subset and whole-sinogram regularization; not specified.
diffusion hyperparameters (T, sigma_max, architecture, training length)
Training details inherited from Song et al. VE-SDE but not reported for this implementation; affect the quality of learned priors.

assumptions (4)

domain assumption CT imaging is linear: x = AI (Eq. 1).
Standard CT model; the system matrix A and Radon transform are assumed known and exact.
domain assumption Score-based SDE framework with VE-SDE learns the true score function.
The paper relies on the standard score-matching result that s_theta approximates grad log p_t; network approximation error is not quantified.
ad hoc to paper Subset division reduces learning difficulty and improves fine-detail reconstruction.
Stated in Section III-A as motivation; no formal guarantee that per-subset models are easier to train or that their combination is superior.
ad hoc to paper Alternating optimization with data consistency reaches a good solution.
Algorithm 1 is a heuristic alternating scheme; convergence to an optimum of Eq. (15) is not established.

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Cite this review

Pith. "Pith review of Ordered-subsets Multi-diffusion Model for Sparse-view CT Reconstruction." pith.science (2026). https://pith.science/paper/EHHFUHIP

@misc{pith2026250509985,
  author       = {Pith},
  title        = {Pith review of: Ordered-subsets Multi-diffusion Model for Sparse-view CT Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EHHFUHIP}},
  note         = {Machine review of arXiv:2505.09985}
}

read the original abstract

Score-based diffusion models have shown significant promise in the field of sparse-view CT reconstruction. However, the projection dataset is large and riddled with redundancy. Consequently, applying the diffusion model to unprocessed data results in lower learning effectiveness and higher learning difficulty, frequently leading to reconstructed images that lack fine details. To address these issues, we propose the ordered-subsets multi-diffusion model (OSMM) for sparse-view CT reconstruction. The OSMM innovatively divides the CT projection data into equal subsets and employs multi-subsets diffusion model (MSDM) to learn from each subset independently. This targeted learning approach reduces complexity and enhances the reconstruction of fine details. Furthermore, the integration of one-whole diffusion model (OWDM) with complete sinogram data acts as a global information constraint, which can reduce the possibility of generating erroneous or inconsistent sinogram information. Moreover, the OSMM's unsupervised learning framework provides strong robustness and generalizability, adapting seamlessly to varying sparsity levels of CT sinograms. This ensures consistent and reliable performance across different clinical scenarios. Experimental results demonstrate that OSMM outperforms traditional diffusion models in terms of image quality and noise resilience, offering a powerful and versatile solution for advanced CT imaging in sparse-view scenarios.

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Pith tools

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