Solving Blind Inverse Problems: Adaptive Diffusion Models for Motion-corrected Sparse-view 4DCT

Alexandre Bousse; Antoine De Paepe; Cl\'ementine Phung-Ngoc; Dimitris Visvikis

REVIEW 4 major objections 5 minor 1 cited by

Solving Blind Inverse Problems: Adaptive Diffusion Models for Motion-corrected Sparse-view 4DCT

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper claims that a diffusion-model prior, combined with on-the-fly calibration of a surrogate-scaled deformation model, solves blind motion-corrected sparse-view 4DCT reconstruction, reporting artifact-free end-inhale images on XCAT…

desk verdict A sensible integration of diffusion priors and surrogate-driven motion estimation for sparse-view 4DCT, with promising phantom results but no validation of the estimated motion fields. read the letter →

arxiv 2501.12249 v4 pith:2RWCXTK6 submitted 2025-01-21 physics.med-ph

Antoine De Paepe , Alexandre Bousse , Clémentine Phung-Ngoc , Dimitris Visvikis This is my paper · ORCID

classification physics.med-ph

keywords 4DCTreconstructionmotioncorrectionblindinverseproblemsdiffusionposteriorsamplingjointandestimationrespiratorysparse-viewcomputedtomographywaveletmodel

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 tries to establish that a blind inverse problem—reconstructing a motion-free 3-D CT image from sparse-view, low-dose 4DCT measurements in which the respiratory deformation fields and surrogate signal are unknown—can be solved by combining a diffusion-model prior with an adaptively calibrated motion model. The proposed method, JRM-ADM, alternates wavelet-domain diffusion posterior sampling with short optimization steps that fit a scalar-surrogate-scaled deformation field to the current image estimate. On five XCAT phantom datasets with irregular breathing, it reports end-inhale reconstructions with PSNR 27.05 ± 0.37 and SSIM 0.94 ± 0.01, outperforming gated filtered backprojection, gated diffusion posterior sampling, and TV-regularized joint reconstruction and motion estimation. If this holds, sparse-view 4DCT could be reconstructed without respiratory gating while preserving resolution, which is exactly the regime relevant to low-dose radiotherapy imaging.

What carries the argument

The adaptive forward model is the central object: $A_{\varphi,s} = [R \circ T_k \circ W_{s_k \varphi}]_k$, a per-time composition of the fan-beam line-integral operator $R$, a slice extractor $T_k$, and a deformation operator $W_{s_k \varphi}$ driven by a shared B-spline DVF scaled by scalar surrogates. The argument is carried by the alternating loop in Algorithm 1: a wavelet-domain diffusion network $v_\theta$ proposes a clean coefficient image, a short RMSprop step fits $(\varphi, s)$ to that proposal through the likelihood, and a data-consistency update in image space produces the next clean estimate before the DDIM step advances. The discrete wavelet transform $V$ is what makes 3-D diffusion tractable, and the jumpstart from a gated FBP image shortens the reverse process.

What would settle it

Run JRM-ADM on a dataset whose ground-truth motion includes spatially varying or inspiratory/expiratory hysteresis—for example, a XCAT phantom with different regional breathing amplitudes or a real patient 4DCT with irregular breathing—and compare end-inhale PSNR and SSIM against JRM-TV and gated-DPS. If JRM-ADM no longer exceeds the comparators or shows residual diaphragm motion artifacts, the central claim that adaptive diffusion models solve blind motion-corrected sparse-view 4DCT is refuted.

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Extended reading notes

Core claim

JRM-ADM's central claim is that one can jointly reconstruct the image and estimate the motion by treating the forward model itself as an unknown that depends on a B-spline deformation vector field $\varphi$ and a surrogate vector $s$, with per-time deformations $\varphi_k = s_k \varphi$. During DDIM sampling in the wavelet domain, the method alternates between estimating the clean image from the diffusion network, calibrating $(\varphi, s)$ by minimizing the weighted negative log-likelihood against that estimate, and enforcing image-domain data consistency. The paper reports that this yields artifact-free, high-resolution end-inhale reconstructions under irregular breathing on XCAT phantom data, with higher PSNR and SSIM than gated-FBP, gated-DPS, and JRM-TV on all five test datasets.

Load-bearing premise

The method assumes every respiratory deformation is a single reference deformation field scaled by a scalar surrogate; if true breathing has spatially varying or hysteretic motion that this one-parameter scaling cannot represent, both the reconstructed image and the estimated motion will be biased.

Editorial extensions

If this is right

The end-inhale phase can be reconstructed without phase gating, removing gating-induced noise amplification and irregular-breathing motion artifacts in the same pass.
Surrogate signals need not be measured during acquisition; the scalar surrogate vector is recovered as part of the reconstruction.
Diffusion priors give the resolution preservation that TV regularization lacks, while still suppressing streak and photon-counting noise.
The Poisson statistical weighting in the data-consistency term carries over to low-dose photon-counting CT, where counts per view are small.
Wavelet-domain diffusion keeps the computationally heavy 3-D problem within feasible memory and runtime budgets.

Reading between the lines

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

The single-deformation-field scaling assumption, $\varphi_k = s_k \varphi$, is the part most likely to break on real patients; a natural extension would be to parameterize motion with two or more DVF components, for example separate inspiratory and expiratory fields, and let the surrogate vector choose their mixture.
The same alternating calibration trick should transfer to other blind inverse problems in medical imaging where the unknown forward operator has a low-dimensional parameterization, such as joint activity and attenuation estimation in PET.
Because the evidence is currently limited to XCAT phantoms that may conform to the motion model, the decisive test is a comparison on real 4DCT or on a phantom with spatially varying or hysteretic motion; the authors state they are working toward real CT volumes.
The jumpstart strategy and five-step RMSprop calibration suggest a robustness question: how sensitive the final image is to the surrogate initialization and the number of calibration iterations could be checked with an ablation across datasets.

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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 core idea is clean: take the joint reconstruction and motion estimation (JRM) framework from Huang et al., combine it with the adaptive blind-inversion diffusion approach of Bai et al., run the diffusion in the wavelet domain to save memory, and solve the combined problem with alternating updates. That integration is non-trivial and the empirical results on five XCAT phantoms are decent. The PSNR/SSIM gains over gated-FBP, gated-DPS, and JRM-TV are consistent across datasets, and the qualitative figure shows visibly cleaner images. The paper is honest about the biggest limitation—training and testing on XCAT phantoms only—and does not pretend to have clinical validation. For a short conference-style paper, the writing is clear and the method is reproducible in principle.

The soft spots are real and load-bearing. The most serious is that the estimated motion fields are never scored. Algorithm 1 updates the B-spline DVF and surrogate signal with only 5 RMSprop iterations per diffusion step, and the paper reports no comparison between the estimated deformations and the true XCAT phase-to-phase motion. Without that internal check, the claim that the method does motion correction is not established; the image-quality gains could come largely from the diffusion prior and from using all 170 frames. The comparison against JRM-TV, which uses the same motion model and full data, isolates the diffusion prior's contribution but not the motion estimation's accuracy. The title says 'solving' the blind inverse problem, which is stronger than what the evidence supports.

The missing baseline to Huang et al. is a mistake. Since the motion model is taken directly from that paper, readers need to see whether JRM-ADM beats the underlying JRM method with a proper convex prior under the same motion model. The TV-based JRM is a useful proxy but not the same thing. Reporting only the end-inhale phase is also selective, though the authors justify it as the phase most affected by motion. Still, showing one more phase would have strengthened the claim. The lack of code and hyperparameters makes the results hard to verify, and the linear surrogate model in Eq. (1) is an assumption that is never tested against richer motion patterns.

None of these issues are disqualifying for a workshop or a conference round. The paper is a reasonable contribution that combines existing ideas in a new way and reports positive preliminary evidence. What it needs is motion-field validation, the missing baseline, more phases, and code release. I would send it to peer review with the expectation of major revision. The reader's take is, in my view, correctly calibrated: conditional, moderate confidence. The stress-test note is right that the motion estimates are unvalidated, and that should be the main thing an editor asks for.

For a colleague working on 4DCT or diffusion-based inverse problems, this is worth a quick read. I would not cite it in my own work yet, until the motion validation appears. But it deserves a serious referee rather than a desk rejection.

Referee Report

4 major / 5 minor

Summary. The paper proposes JRM-ADM, a diffusion-model-based framework for joint reconstruction and motion estimation (JRM) in sparse-view 4DCT. Respiratory motion is modeled by a single deformation field φ scaled by a scalar surrogate signal s_k per time frame (φ_k = s_k·φ), and the forward model is calibrated adaptively during diffusion posterior sampling. The method operates in a wavelet latent space to reduce memory and computation, and it alternates between data-consistency updates of the image and RMSprop-based updates of (φ,s). Experiments on five XCAT phantoms report PSNR and SSIM for the end-inhale phase, showing improvements over gated-FBP, gated-DPS, and JRM-TV. The paper claims artifact-free, high-resolution reconstructions under irregular breathing conditions, while acknowledging the lack of real 4DCT validation.

Significance. If the results are substantiated, the paper makes a useful contribution by combining diffusion priors with motion-corrected 4DCT reconstruction and by addressing the computational cost through the wavelet-domain formulation. The pseudo-code and the explicit treatment of the blind inverse problem are helpful. However, the current evidence is limited to synthetic XCAT data, and the absence of any quantitative validation of the estimated deformation fields means the central 'motion-corrected' claim is not yet established. The reported image metrics alone cannot distinguish accurate motion estimation from the effect of the diffusion prior and multi-frame data consistency. The paper is clearly written and the computational direction is relevant, but the evaluation gaps are substantial enough to require revision before the findings can be considered reliable.

major comments (4)

[Section 3.2 and Algorithm 1] The estimated deformation field φ and surrogate signal s are never compared to the ground-truth motion used to generate the five XCAT test datasets. Because Eq. (1) imposes a strong model (φ_k = s_k·φ) and Algorithm 1 (lines 7 and 13) performs only 5 RMSprop iterations for both the motion and image updates, the reported PSNR/SSIM gains cannot be attributed to accurate motion estimation. Please report quantitative motion errors (e.g., DVF endpoint error, surrogate correlation) for the test phantoms. The Section 4 limitation about XCAT training does not address this internal validation gap.
[Section 3.1 and Table 1] The evaluation is restricted to a single end-inhale phase, and the paper never states how the end-inhale image was formed from the method's output (x̂0, φ̂, ŝ). If PSNR/SSIM are computed on W_{ŝ_k φ̂}(x̂0) for the end-inhale index k, this warping step should be described explicitly, and the same pipeline should be applied to multiple phases or a time-averaged error. Per-phase metrics are necessary to support the general claim of motion-corrected 4DCT reconstruction across the respiratory cycle.
[Section 3.1 and Table 1] The most relevant baseline, Huang et al. [2] (surrogate-optimized JRM without diffusion), is cited and used as the basis of the motion model but is not included in the comparison. Without this baseline, the abstract's claim that the method 'outperforms existing techniques' overstates the evidence. Please add this baseline or clearly justify its omission.
[Section 3.2 and Table 1] The comparison against JRM-TV does not isolate the contribution of the adaptive forward-model calibration, since JRM-TV uses the same all-frame data and the same motion model. An ablation that fixes (φ,s) to the gated estimates or runs the diffusion prior without the per-step calibration would demonstrate the value of the adaptive component, which is the paper's central novelty.

minor comments (5)

[Section 2.2.2] The sentence 'performing the diffusion in a the wavelet domain' should read 'performing the diffusion in the wavelet domain.'
[Section 3.2] 'This results are confirmed' should be 'These results are confirmed.'
[Algorithm 1] The notation is incomplete: the Require line lists {α_t}_{t=1}^{T'} but the update in line 10 uses α_{t−δt}, and the relationship between δt and the α index is not defined.
[Section 3.1] Hyperparameters that materially affect the method are not reported: the data-consistency weight schedule ζ_t, the number of RMSprop iterations for lines 7 and 13, the B-spline control-point grid, and the initial surrogate signal s. Providing these values is important for reproducibility.
[Section 2.2.3] The phrase 'standard sinusoidal signal to initialize s' is vague; please specify the amplitude, frequency, and how the phase is aligned with the acquired data.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the motion model and forward-model fit are explicit assumptions from external work, and the XCAT train/test overlap is a generalization limitation, not a circular derivation; the sole self-citation is non-load-bearing.

full rationale

The derivation chain is self-contained and not circular. The motion model φ_k = s_k · φ is introduced as an explicit assumption in Eq. (1), borrowed from external work [1,2], and is not derived from the target reconstruction. Eq. (12) estimates (φ,s) from the current diffusion estimate x̂_{0|t}, and Eq. (13) enforces data consistency; this is a standard blind-inverse-problem fit, and the reported PSNR/SSIM are computed against XCAT ground truth, not against the fitted parameters. The diffusion prior is trained on XCAT phantoms and evaluated on separately generated XCAT morphologies; this is a train/test distribution match that can inflate apparent performance and limits claims about real CT, and the paper's Section 4 limitation ('our models were trained and evaluated on XCAT phantoms due to the limited availability of 4DCT datasets') is acknowledged. But it is not a circular derivation: the measurements y are still required, and the reconstruction is not identical to a training image by construction. The only self-citation, [17], appears in the Discussion to support 'generalizability to unseen data'; the paper's own held-out XCAT test already provides direct evidence for generalization to unseen phantom morphologies, so the self-citation is not load-bearing. No uniqueness theorem or ansatz is imported from the authors' own prior work. The absence of quantitative validation of the estimated motion fields is a substantive correctness/internal-validity gap, but it does not make the image-reconstruction claim circular.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The method relies on standard CT physics (Beer-Lambert, Poisson), the penalized weighted least squares approximation, and the surrogate-scaled motion model. The key domain assumption is that all respiratory motion is a single DVF scaled by a scalar surrogate (Eq. 1). The diffusion prior is learned from XCAT data, which is a strong assumption for generalization. Several hyperparameters (ζ_t, RMSprop iterations, T', δt) are chosen by hand and not justified.

free parameters (5)

Data consistency weight schedule ζ_t = Not specified in the paper
Controls the balance between the diffusion prior and measurement fidelity in Eq. (13); the schedule is not reported, so it may have been tuned on the evaluation data.
Number of RMSprop iterations for motion and data-consistency updates = 5
Chosen by hand without justification; affects convergence of the alternating optimization.
Jumpstart timestep T' and DDIM step δt = T'=300, δt=10
Hand-chosen hyperparameters that control the diffusion sampling trajectory.
Initial surrogate signal s = Sinusoidal
The surrogate signal is initialized as a standard sinusoid; the result may depend on this initial guess, especially for irregular breathing.
B-spline control point grid for φ = Not specified
The deformation field is parameterized by B-splines, but the control point spacing is not given, which is a free modeling choice.

assumptions (5)

standard math Beer-Lambert law with Poisson noise (Eq. 2-3)
Standard CT measurement model for photon counting.
standard math Penalized weighted least squares approximation of the negative log-posterior (Eq. 5)
From Elbakri et al. [7]; used to justify the data-fidelity terms.
domain assumption Surrogate-scaled single DVF motion model φ_k = s_k·φ (Eq. 1)
Assumes all respiratory motion is a single deformation field scaled by a scalar surrogate; not validated against richer motion.
domain assumption The DWT is bijective
Used to switch between image and wavelet domains in Eq. (13); bijectivity depends on the specific wavelet, which is not specified.
domain assumption The diffusion prior trained on XCAT generalizes to unseen XCAT morphologies
The prior is trained on the same simulator used for evaluation; generalization to real CT is not established.

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Cite this review

Pith. "Pith review of Solving Blind Inverse Problems: Adaptive Diffusion Models for Motion-corrected Sparse-view 4DCT." pith.science (2026). https://pith.science/paper/2RWCXTK6

@misc{pith2026250112249,
  author       = {Pith},
  title        = {Pith review of: Solving Blind Inverse Problems: Adaptive Diffusion Models for Motion-corrected Sparse-view 4DCT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2RWCXTK6}},
  note         = {Machine review of arXiv:2501.12249}
}

read the original abstract

Four-dimensional computed tomography (4DCT) is essential for medical imaging applications like radiotherapy, which demand precise respiratory motion representation. Traditional methods for reconstructing 4DCT data suffer from artifacts and noise, especially in sparse-view, low-dose contexts. Motion-corrected (MC) reconstruction is a blind inverse problem that we propose to solve with a novel diffusion model (DM) framework that calibrates an adaptive unknown forward model for motion correction. Furthermore, we used a wavelet diffusion model (WDM) to address computational cost and memory usage. By leveraging the prior probability distribution function (PDF) from the DMs, we enhance the joint reconstruction and motion estimation (JRM) process, improving image quality and preserving resolution. Experiments on extended cardiac-torso (XCAT) phantom data demonstrate that our method outperforms existing techniques, yielding artifact-free, high-resolution reconstructions even under irregular breathing conditions. These results showcase the potential of combining DMs with motion correction to advance sparse-view 4DCT imaging.

Figures

Figures reproduced from arXiv: 2501.12249 by the authors.

**Figure 1.** Summary of JRM-ADM. which eliminates the need to backpropagate through vθ and is solved with 5 RMSprop iterations. The new clean estimate v˜0|t ≜ V(x˜0|t) is then used to sample vt−1 using (8) in the wavelet domain. The overall method, which we name JRM-ADM, is summarized in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** GT and end-inhale phase reconstructions. of the diffusion prior. However, they both suffer from motion artifacts around the diaphragm due to irregular breathing motion. JRM-TV produces noise-free and streak-free images, thanks to the TV regularization. Furthermore, JRM-TV avoids motion artifacts as it does not rely on gating. Nonetheless, it is limited by poor resolution, a consequence of the TV regularization. On t… view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [2]

Resolving Variable Respiratory Motion From Unsorted 4D Computed Tomography

Y. Huang, B. Eiben, K. Thielemans, et al. “Resolving Variable Respiratory Motion From Unsorted 4D Computed Tomography”.International Conference on Medical Image Computing and Computer-Assisted Intervention. Springer. 2024, pp. 588–597

work page 2024

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work page 2017

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arXiv doi:10.48550/arxiv.2209.14687 2023

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doi:10.1093/bjrai/ubae013 2024

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Y. Hu, A. Peng, W. Gan, et al. “ADOBI: Adaptive Diffusion Bridge For Blind Inverse ProblemswithApplicationtoMRIReconstruction”. arXivpreprintarXiv:2411.16535 (2024)

work page Pith review arXiv 2024

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P. Friedrich, J. Wolleb, F. Bieder, et al. “WDM: 3D wavelet diffusion models for high-resolution medical image synthesis”.MICCAI Workshop on Deep Generative Models. Springer. 2024, pp. 11–21

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Denoising diffusion probabilistic models

J. Ho, A. Jain, and P. Abbeel. “Denoising diffusion probabilistic models”.Advances inneuralinformationprocessingsystems 33(2020),pp.6840–6851. doi: 10.48550/ arXiv.2006.11239

arXiv doi:10.48550/arxiv.2006.11239 2020