pith. sign in

arxiv: 2606.02309 · v1 · pith:RKUZYUVLnew · submitted 2026-06-01 · 💻 cs.LG · cs.CV

Measurement Geometry and Design for Trustworthy Generative Inverse Problems

Pengfei Jin , Na Li , Quanzheng Li This is my paper

Pith reviewed 2026-06-28 15:07 UTC · model grok-4.3

classification 💻 cs.LG cs.CV
keywords generative inverse problemsmeasurement designmanifold compatibilitytrustworthy reconstructionMRI samplingacquisition rules
0
0 comments X

The pith

A local compatibility measure between measurements and generative priors controls the stable part of reconstruction error.

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

The paper establishes a measurement-geometry view of generative inverse problems. It defines a local measurement-manifold compatibility measure to check whether a fixed operator distinguishes nearby plausible images. The proof shows this measure governs stable error under local regularity while the prior handles drift off the manifold. Practical designs follow from volume preservation, including test-time adaptation. Experiments confirm it predicts hallucinations and improves sampling in MRI.

Core claim

Under local regularity assumptions, the local measurement-manifold compatibility measure controls the stable part of the reconstruction error in generative inverse problems, while the generative prior controls off-manifold drift. This worst-direction certificate leads to acquisition rules based on local volume preservation.

What carries the argument

The local measurement-manifold compatibility measure, which quantifies how well the measurement operator observes prior-relevant tangent directions on the generative manifold.

If this is right

  • The measure predicts failure modes across row-sampling, tomographic, and MR acquisition.
  • It explains measurement-induced hallucinations in reconstructions.
  • Posterior-cloud design at test time improves over variable-density and Poisson-like masks in fastMRI.
  • Fixed and sequential acquisition rules can be derived from overall local volume preservation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The certificate may inform operator design in other inverse problems beyond imaging.
  • Posterior-cloud adaptation provides a test-time way to handle uncertainty without learning a policy.
  • The volume preservation idea could extend to sequential decisions in dynamic settings.

Load-bearing premise

Local regularity assumptions on the generative prior and measurement operator that relate the compatibility measure to stable error.

What would settle it

A counterexample where high compatibility measure coincides with large stable reconstruction error would falsify the main theorem.

Figures

Figures reproduced from arXiv: 2606.02309 by Na Li, Pengfei Jin, Quanzheng Li.

Figure 1
Figure 1. Figure 1: Overview of measurement geometry and design. (A) A generative prior induces a data [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: MNIST row sampling: hallucination, fixed-mask design, and geometry-error relationship. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Adaptive measurement design in row sampling and CT. (A) MNIST row posterior-cloud [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Representative MR Cartesian sampling example. The left panel shows the ground truth; [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Additional MNIST row-inpainting examples under the fixed stride-4 row operator used in [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Additional fixed-row design examples corresponding to Figure 2(a). Each block compares [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Logdet score versus DPS relative error for the fixed-row design study, corresponding to [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Second-stage row-selection heatmap for posterior-cloud adaptive MNIST acquisition. The [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Additional fixed-row geometry diagnostic: empirical [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: MNIST-CT posterior-cloud angle-selection gallery for the [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Additional copy of the representative MR visualization in Figure 4, sample 037. The [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Additional MR example, sample 018. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Additional MR example, sample 034. M0 uniform M1 random×3 M2 ours k36 M5 ACS+Gauss M6 ACS+Poisson-like GLOBAL p37+a16 NRMSE 0.0949 SSIM 0.942 PSNR 34.65 NRMSE 0.0857 SSIM 0.945 PSNR 35.62 NRMSE 0.0786 SSIM 0.955 PSNR 36.28 NRMSE 0.0583 SSIM 0.966 PSNR 38.95 NRMSE 0.0509 SSIM 0.971 PSNR 40.06 NRMSE 0.0486 SSIM 0.973 PSNR 40.47 sample_idx=45 (~q05 GLOBAL seed-mean NRMSE) | GT shared across methods | stochas… view at source ↗
Figure 14
Figure 14. Figure 14: Additional MR example, sample 045. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Additional MR example, sample 073. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_15.png] view at source ↗
read the original abstract

Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions. This distinction is especially important in medical imaging, where acquisition operators are designed under scan-time, dose, and calibration constraints. We study generative inverse problems from a measurement-geometry perspective. The central question is whether a fixed measurement operator can distinguish nearby images that are plausible under the generative prior, and whether this relationship can guide better measurements. We introduce a local measurement-manifold compatibility measure that quantifies how well the operator observes prior-relevant tangent directions. Under local regularity assumptions, we prove that this quantity controls the stable part of the reconstruction error, while the generative prior controls off-manifold drift. This worst-direction certificate motivates practical fixed and sequential acquisition rules based on overall local volume preservation, including a posterior-cloud design that adapts measurements at test time without training a sampling policy. Across row-sampling, tomographic, and MR acquisition settings, the proposed scores predict failure modes, explain measurement-induced hallucinations, and guide better sampling. In fastMRI Cartesian sampling, posterior-cloud measurement design improves over strong non-learned ACS-preserving baselines, including variable-density and Poisson-like masks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a local measurement-manifold compatibility measure for generative inverse problems. Under local regularity assumptions on the generative prior and measurement operator, it proves that this measure controls the stable component of reconstruction error while the prior governs off-manifold drift. The measure motivates fixed and sequential acquisition designs, including a test-time posterior-cloud method. Experiments across row-sampling, tomography, MR, and fastMRI settings show that the scores predict failure modes and that the posterior-cloud design improves over non-learned baselines such as variable-density and Poisson-like masks in fastMRI Cartesian sampling.

Significance. If the central theorem holds with verified assumptions, the work supplies a geometric certificate linking measurement design to trustworthy reconstruction in generative inverse problems, with direct relevance to constrained medical imaging. The combination of a local volume-preservation design rule and empirical gains over strong baselines is a concrete contribution; the absence of parameter-free derivations or machine-checked proofs is offset by the falsifiable prediction that the compatibility score should correlate with stable error under the stated conditions.

major comments (2)
  1. [Abstract, §3] Abstract and §3 (theorem statement): the proof that the compatibility measure controls stable reconstruction error is conditioned on local regularity assumptions (manifold smoothness, bounded curvature, Lipschitz constants of the restricted operator in tangent neighborhoods). The experiments in §4–5 apply the method to standard generative models and operators (row-sampling, tomography, MR, fastMRI) yet report no verification or diagnostic that these local conditions hold at the operating points. If the assumptions are violated, the claimed certificate and derived design rules lack theoretical grounding for the concrete results.
  2. [§4] §4 (experimental setup): the manuscript provides no quantitative error analysis or ablation that isolates the contribution of the compatibility measure from the generative prior itself. Without such controls, it is difficult to assess whether observed improvements in fastMRI are attributable to the geometry-based design or to other factors such as mask density.
minor comments (2)
  1. [§2] Notation for the compatibility measure and tangent-space projections should be introduced with an explicit equation early in §2 to avoid ambiguity when the measure is later used in the theorem.
  2. [§5] Figure captions for the fastMRI results should include the exact number of test slices and the precise definition of the ACS-preserving baseline masks for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and will incorporate revisions to strengthen the connection between theory and experiments.

read point-by-point responses

  1. Referee: [Abstract, §3] Abstract and §3 (theorem statement): the proof that the compatibility measure controls stable reconstruction error is conditioned on local regularity assumptions (manifold smoothness, bounded curvature, Lipschitz constants of the restricted operator in tangent neighborhoods). The experiments in §4–5 apply the method to standard generative models and operators (row-sampling, tomography, MR, fastMRI) yet report no verification or diagnostic that these local conditions hold at the operating points. If the assumptions are violated, the claimed certificate and derived design rules lack theoretical grounding for the concrete results.

    Authors: We agree that explicit verification of the local regularity assumptions would strengthen the grounding of the theoretical claims in the concrete experiments. In the revised manuscript we will add a dedicated diagnostics subsection (new §4.1) that reports empirical estimates of local Lipschitz constants (via finite differences along estimated tangent spaces), curvature bounds (via second-order finite differences), and manifold smoothness indicators for the generative models at the operating points used in §4–5. These checks will either confirm the assumptions hold approximately or identify regimes where they are mildly violated, with discussion of the implications for the certificate. revision: yes

  2. Referee: [§4] §4 (experimental setup): the manuscript provides no quantitative error analysis or ablation that isolates the contribution of the compatibility measure from the generative prior itself. Without such controls, it is difficult to assess whether observed improvements in fastMRI are attributable to the geometry-based design or to other factors such as mask density.

    Authors: We acknowledge the absence of isolating ablations. In the revision we will add quantitative controls in §4 and the fastMRI experiments of §5: (i) fixed-prior comparisons of compatibility-guided masks versus density-matched random and variable-density masks, reporting both total and stable-component reconstruction error; (ii) an ablation that varies only the measurement design while holding the generative prior fixed; and (iii) a non-generative baseline (e.g., compressed-sensing reconstruction) to separate prior-driven from measurement-driven effects. These will clarify the incremental contribution of the compatibility measure. revision: yes

Circularity Check

0 steps flagged

No circularity; new measure defined and theorem proved independently under stated assumptions.

full rationale

The paper defines a local measurement-manifold compatibility measure and states a theorem that, under local regularity assumptions on the generative prior and measurement operator, this quantity controls the stable part of reconstruction error. No equations or steps reduce the claimed control to a fitted parameter, self-definition, or self-citation chain. The derivation introduces the quantity explicitly and derives its error-control property from the assumptions rather than by construction or renaming. Experiments apply the measure but do not alter the logical independence of the theorem. This is the normal case of a self-contained theoretical contribution.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Central claim rests on local regularity assumptions invoked for the error-control proof and on the newly defined compatibility measure; no free parameters or invented physical entities are mentioned.

axioms (1)
  • domain assumption local regularity assumptions
    Invoked to prove that the compatibility measure controls the stable part of reconstruction error.
invented entities (1)
  • local measurement-manifold compatibility measure no independent evidence
    purpose: Quantifies how well the operator observes prior-relevant tangent directions.
    Newly introduced quantity whose properties are proved under the regularity assumptions.

pith-pipeline@v0.9.1-grok · 5760 in / 1160 out tokens · 24594 ms · 2026-06-28T15:07:46.920140+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

42 extracted references · 14 canonical work pages

  1. [1]

    Dimakis, and Jonathan I

    Asad Aali, Giannis Daras, Brett Levac, Sidharth Kumar, Alexandros G. Dimakis, and Jonathan I. Tamir. Ambient diffusion posterior sampling: Solving inverse problems with diffusion models trained on corrupted data, 2024. URLhttps://arxiv.org/abs/2403.08728

    arXiv 2024

  2. [2]

    Wang, Adrian V

    Cagla Deniz Bahadir, Alan Q. Wang, Adrian V. Dalca, and Mert R. Sabuncu. Deep-learning- based optimization of the under-sampling pattern in mri.IEEE Transactions on Computational Imaging, 6:1139–1152, 2020. doi: 10.1109/TCI.2020.3006727. URLhttps://doi.org/10.1109/ TCI.2020.3006727. 11

    work page doi:10.1109/tci.2020.3006727 2020

  3. [3]

    Ashish Bora, Ajil Jalal, Eric Price, and Alexandros G. Dimakis. Compressed sensing using generative models. InProceedings of the 34th International Conference on Machine Learning, volume 70 ofProceedings of Machine Learning Research, pages 537–546. PMLR, 2017. URL https://proceedings.mlr.press/v70/bora17a.html

    2017

  4. [4]

    Candès, Justin Romberg, and Terence Tao

    Emmanuel J. Candès, Justin Romberg, and Terence Tao. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information.IEEE Transactions on Information Theory, 52(2):489–509, 2006. doi: 10.1109/TIT.2005.862083. URLhttps: //doi.org/10.1109/TIT.2005.862083

    work page doi:10.1109/tit.2005.862083 2006

  5. [5]

    Cheng, Feiyu Chen, Christopher Sandino, Morteza Mardani, John M

    Joseph Y. Cheng, Feiyu Chen, Christopher Sandino, Morteza Mardani, John M. Pauly, and Shreyas S. Vasanawala. Compressed sensing: From research to clinical practice with data-driven learning, 2019. URLhttps://arxiv.org/abs/1903.07824

    Pith/arXiv arXiv 2019

  6. [6]

    Score-based diffusion models for accelerated mri.Medical Image Analysis, 80:102479, 2022

    Hyungjin Chung and Jong Chul Ye. Score-based diffusion models for accelerated mri.Medical Image Analysis, 80:102479, 2022. doi: 10.1016/j.media.2022.102479. URLhttps://doi.org/ 10.1016/j.media.2022.102479

    work page doi:10.1016/j.media.2022.102479 2022

  7. [7]

    Improv- ing diffusion models for inverse problems using manifold constraints

    Hyungjin Chung, Byeongsu Sim, Dohoon Ryu, and Jong Chul Ye. Improv- ing diffusion models for inverse problems using manifold constraints. InAd- vances in Neural Information Processing Systems, volume 35, pages 25683–25696,

  8. [8]

    URL https://proceedings.neurips.cc/paper_files/paper/2022/hash/ a48e5877c7bf86a513950ab23b360498-Abstract-Conference.html

    2022

  9. [9]

    Klasky, and Jong Chul Ye

    Hyungjin Chung, Jeongsol Kim, Michael Thompson McCann, Marc L. Klasky, and Jong Chul Ye. Diffusion posterior sampling for general noisy inverse problems. InThe Eleventh International Conference on Learning Representations, 2023. URLhttps://openreview.net/forum?id= OnD9zGAGT0k

    2023

  10. [10]

    McCann, Marc L

    Hyungjin Chung, Dohoon Ryu, Michael T. McCann, Marc L. Klasky, and Jong Chul Ye. Solving 3d inverse problems using pre-trained 2d diffusion models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22542–22551,

  11. [11]

    URL https://openaccess.thecvf.com/content/CVPR2023/html/Chung_Solving_3D_ Inverse_Problems_Using_Pre-Trained_2D_Diffusion_Models_CVPR_2023_paper.html

  12. [12]

    Dimakis, and Mauricio Delbracio

    Giannis Daras, Hyungjin Chung, Chieh-Hsin Lai, Yuki Mitsufuji, Jong Chul Ye, Peyman Milanfar, Alexandros G. Dimakis, and Mauricio Delbracio. A survey on diffusion models for inverse problems, 2024. URLhttps://arxiv.org/abs/2410.00083

    Pith/arXiv arXiv 2024

  13. [13]

    Constant-expansion suffices for compressed sensing with generative priors

    Constantinos Daskalakis, Dhruv Rohatgi, and Emmanouil Zampetakis. Constant-expansion suffices for compressed sensing with generative priors. InAdvances in Neural Information Processing Systems, volume 33, 2020. URLhttps://proceedings.neurips.cc/paper/2020/ hash/9fa83fec3cf3810e5680ed45f7124dce-Abstract.html

    2020

  14. [14]

    Diffusion models beat gans on image synthesis.Advances in Neural Information Processing Systems, 34: 8780–8794, 2021

    Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis.Advances in Neural Information Processing Systems, 34: 8780–8794, 2021. URL https://proceedings.neurips.cc/paper/2021/hash/ 49ad23d1ec9fa4bd8d77d02681df5cfa-Abstract.html

    2021

  15. [15]

    David L. Donoho. Compressed sensing.IEEE Transactions on Information Theory, 52(4): 1289–1306, 2006. doi: 10.1109/TIT.2006.871582. URLhttps://doi.org/10.1109/TIT.2006. 871582. 12

    work page doi:10.1109/tit.2006.871582 2006

  16. [16]

    Diffusion posterior sampling for linear inverse problem solving: A filtering perspective

    Zehao Dou and Yang Song. Diffusion posterior sampling for linear inverse problem solving: A filtering perspective. InThe Twelfth International Conference on Learning Representations,

  17. [17]

    URLhttps://openreview.net/forum?id=tplXNcHZs1

  18. [18]

    Baron, Ethan M

    Nicholas Dwork, Corey A. Baron, Ethan M. I. Johnson, Daniel O’Connor, John M. Pauly, and Peder E. Z. Larson. Fast variable density poisson-disc sample generation with directional variation for compressed sensing in mri.Magnetic Resonance Imaging, 77:186–193, 2021. doi: 10.1016/j.mri.2020.11.012. URLhttps://doi.org/10.1016/j.mri.2020.11.012

    work page doi:10.1016/j.mri.2020.11.012 2021

  19. [19]

    Learning-based compressive mri.IEEE Transactions on Medical Imaging, 37(6):1394–1406, 2018

    Baran Gözcü, Rabeeh Karimi Mahabadi, Yen-Huan Li, Efe Ilıcak, Tolga Çukur, Jonathan Scarlett, and Volkan Cevher. Learning-based compressive mri.IEEE Transactions on Medical Imaging, 37(6):1394–1406, 2018. doi: 10.1109/TMI.2018.2832540. URLhttps://doi.org/10. 1109/TMI.2018.2832540

    work page doi:10.1109/tmi.2018.2832540 2018

  20. [20]

    Griswold, Peter M

    Mark A. Griswold, Peter M. Jakob, Robin M. Heidemann, Mathias Nittka, Vladimir Jellus, Jianmin Wang, Berthold Kiefer, and Axel Haase. Generalized autocalibrating partially parallel acquisitions (grappa).Magnetic Resonance in Medicine, 47(6):1202–1210, 2002. doi: 10.1002/ mrm.10171. URLhttps://doi.org/10.1002/mrm.10171

    work page doi:10.1002/mrm.10171 2002

  21. [21]

    Denoising diffusion probabilis- tic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilis- tic models. InAdvances in Neural Information Processing Systems, volume 33, pages 6840–6851, 2020. URL https://proceedings.neurips.cc/paper/2020/hash/ 4c5bcfec8584af0d967f1ab10179ca4b-Abstract.html

    2020

  22. [22]

    Deep learning-based solvability of underdetermined inverse problems in medical imaging.Medical Image Analysis, 69:101967, 2021

    Chang Min Hyun, Seong Hyeon Baek, Mingyu Lee, Sung Min Lee, and Jin Keun Seo. Deep learning-based solvability of underdetermined inverse problems in medical imaging.Medical Image Analysis, 69:101967, 2021. doi: 10.1016/j.media.2021.101967. URLhttps://doi.org/ 10.1016/j.media.2021.101967

    work page doi:10.1016/j.media.2021.101967 2021

  23. [23]

    Dimakis, and Constantine Caramanis

    Ajil Jalal, Liu Liu, Alexandros G. Dimakis, and Constantine Caramanis. Robust com- pressed sensing using generative models. InAdvances in Neural Information Process- ing Systems, volume 33, 2020. URLhttps://proceedings.neurips.cc/paper/2020/hash/ 07cb5f86508f146774a2fac4373a8e50-Abstract.html

    2020

  24. [24]

    Dimakis, and Jonathan Tamir

    Ajil Jalal, Marius Arvinte, Giannis Daras, Eric Price, Alexandros G. Dimakis, and Jonathan Tamir. Robust compressed sensing mri with deep generative priors. InAdvances in Neural Infor- mation Processing Systems, volume 34, pages 14938–14954, 2021. URLhttps://proceedings. neurips.cc/paper/2021/hash/7d6044e95a16761171b130dcb476a43e-Abstract.html

    2021

  25. [25]

    Denoising diffu- sion restoration models

    Bahjat Kawar, Michael Elad, Stefano Ermon, and Jiaming Song. Denoising diffu- sion restoration models. InAdvances in Neural Information Processing Systems, vol- ume 35, 2022. URL https://proceedings.neurips.cc/paper_files/paper/2022/hash/ 95504595b6169131b6ed6cd72eb05616-Abstract-Conference.html

    2022

  26. [26]

    Tackling hallucination from conditional models for medical image reconstruction with dynamicdps

    Seunghoi Kim, Henry FJ Tregidgo, Matteo Figini, Chen Jin, Sarang Joshi, and Daniel C Alexander. Tackling hallucination from conditional models for medical image reconstruction with dynamicdps. InInternational Conference on Medical Image Computing and Computer- Assisted Intervention, pages 593–603. Springer, 2025

    2025

  27. [27]

    Michael Lustig, David Donoho, and John M. Pauly. Sparse mri: The application of compressed sensing for rapid mr imaging.Magnetic Resonance in Medicine, 58(6):1182–1195, 2007. doi: 10.1002/mrm.21391. URLhttps://doi.org/10.1002/mrm.21391. 13

    work page doi:10.1002/mrm.21391 2007

  28. [28]

    A variational perspective on solving inverse problems with diffusion models

    Morteza Mardani, Jiaming Song, Jan Kautz, and Arash Vahdat. A variational perspective on solving inverse problems with diffusion models. InThe Twelfth International Conference on Learning Representations, 2024. URLhttps://openreview.net/forum?id=1YO4EE3SPB

    2024

  29. [29]

    Nguyen, Gauri Jagatap, and Chinmay Hegde

    Thanh V. Nguyen, Gauri Jagatap, and Chinmay Hegde. Provable compressed sensing with generative priors via langevin dynamics.IEEE Transactions on Information Theory, 68(11): 7410–7422, 2022. doi: 10.1109/TIT.2022.3179643. URLhttps://doi.org/10.1109/TIT.2022. 3179643

    work page doi:10.1109/tit.2022.3179643 2022

  30. [30]

    Pruessmann, Markus Weiger, Markus B

    Klaas P. Pruessmann, Markus Weiger, Markus B. Scheidegger, and Peter Boesiger. Sense: Sensitivity encoding for fast mri.Magnetic Resonance in Medicine, 42(5):952–962, 1999. doi: 10.1002/(SICI)1522-2594(199911)42:5<952::AID-MRM16>3.0.CO;2-S. URL https://doi. org/10.1002/(SICI)1522-2594(199911)42:5%3C952::AID-MRM16%3E3.0.CO;2-S

    work page doi:10.1002/(sici)1522-2594(199911)42:5 1999

  31. [31]

    Adaptive sampling design for compressed sensing mri

    Saiprasad Ravishankar and Yoram Bresler. Adaptive sampling design for compressed sensing mri. In2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pages 3751–3755. IEEE, 2011. doi: 10.1109/IEMBS.2011.6090639. URL https://doi.org/10.1109/IEMBS.2011.6090639

    work page doi:10.1109/iembs.2011.6090639 2011

  32. [32]

    Pseudoinverse-guided diffusion models for inverse problems

    Jiaming Song, Arash Vahdat, Morteza Mardani, and Jan Kautz. Pseudoinverse-guided diffusion models for inverse problems. InInternational Conference on Learning Representations, 2022. URLhttps://openreview.net/forum?id=9_gsMA8MRKQ

    2022

  33. [33]

    Solving inverse problems in medical imaging with score-based generative models, 2021

    Yang Song, Liyue Shen, Lei Xing, and Stefano Ermon. Solving inverse problems in medical imaging with score-based generative models, 2021. URLhttps://arxiv.org/abs/2111.08005

    arXiv 2021

  34. [34]

    Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole

    Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021. URLhttps://openreview.net/ forum?id=PxTIG12RRHS

    2021

  35. [35]

    Rods: Robust optimization inspired diffusion sampling for detecting and reducing hallucination in generative models

    Yiqi Tian, Pengfei Jin, Mingze Yuan, Na Li, Bo Zeng, and Quanzheng Li. Rods: Robust optimization inspired diffusion sampling for detecting and reducing hallucination in generative models. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems

  36. [36]

    Murphy, Patrick Virtue, Michael Elad, John M

    Martin Uecker, Peng Lai, Mark J. Murphy, Patrick Virtue, Michael Elad, John M. Pauly, Shreyas S. Vasanawala, and Michael Lustig. Espirit–an eigenvalue approach to autocalibrating parallel mri: Where sense meets grappa.Magnetic Resonance in Medicine, 71(3):990–1001,

  37. [37]

    Murphy, Patrick Virtue, Michael Elad, John M

    doi: 10.1002/mrm.24751. URLhttps://doi.org/10.1002/mrm.24751

    work page doi:10.1002/mrm.24751

  38. [38]

    Zero-shot image restoration using denoising diffusion null-space model, 2022

    Yinhuai Wang, Jiwen Yu, and Jian Zhang. Zero-shot image restoration using denoising diffusion null-space model, 2022. URLhttps://arxiv.org/abs/2212.00490

    arXiv 2022

  39. [39]

    Compressed sensing mri: A review from signal processing perspective.BMC Biomedical Engineering, 1(1):8, 2019

    Jong Chul Ye. Compressed sensing mri: A review from signal processing perspective.BMC Biomedical Engineering, 1(1):8, 2019. doi: 10.1186/s42490-019-0006-z. URLhttps://doi.org/ 10.1186/s42490-019-0006-z

    work page doi:10.1186/s42490-019-0006-z 2019

  40. [40]

    Muckley, Aaron Defazio, Ruben Stern, Patricia Johnson, Mary Bruno, Marc Parente, Krzysztof J

    Jure Zbontar, Florian Knoll, Anuroop Sriram, Tullie Murrell, Zhengnan Huang, Matthew J. Muckley, Aaron Defazio, Ruben Stern, Patricia Johnson, Mary Bruno, Marc Parente, Krzysztof J. Geras, Joe Katsnelson, Hersh Chandarana, Zizhao Zhang, Michal Drozdzal, Adriana Romero, Michael Rabbat, Pascal Vincent, Nafissa Yakubova, James Pinkerton, Duo Wang, Erich Owen...

    2018

  41. [41]

    Denoising diffusion models for plug-and-play image restoration

    Yuanzhi Zhu, Kai Zhang, Jingyun Liang, Jiezhang Cao, Bihan Wen, Radu Timofte, and Luc Van Gool. Denoising diffusion models for plug-and-play image restoration. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1219–1229,

  42. [42]

    15 A Proof Details This appendix collects the proof details that are abbreviated in Section 4

    URL https://openaccess.thecvf.com/content/CVPR2023/html/Zhu_Denoising_ Diffusion_Models_for_Plug-and-Play_Image_Restoration_CVPR_2023_paper.html. 15 A Proof Details This appendix collects the proof details that are abbreviated in Section 4. A.1 Regularizer Models For the generator-induced penalty, assume thatGθ is a local immersion atz∗ and that x∗ = Gθ(z...

    arXiv 2000