Pith. sign in

REVIEW 3 minor 79 references

Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems

T0 review · 0 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper constructs conformal bounds on full-reference image quality that hold with probability at least 1-alpha when the true image is unknown.

desk verdict A clean, honest application of split conformal prediction to a new target—full-reference image quality—with solid experiments; the novelty is modest but the execution is careful and the claims are appropriately scoped. read the letter →

arxiv 2505.09528 v1 pith:4CLQ7AAJ submitted 2025-05-14 cs.CV

Jeffrey Wen , Rizwan Ahmad , Philip Schniter This is my paper · ORCID
classification cs.CV
keywords conformalpredictionfull-referenceimagequalityrecoveryinverseproblemsuncertaintyquantificationposteriorsamplingacceleratedMRIassessment
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

The paper asks how a user can know the quality of a recovered image when the true image is unavailable. It shows that split conformal prediction can convert a calibration set of known image/measurement pairs into a one-sided bound on any full-reference metric, with a user-chosen error probability. The bound adapts to the test measurements and reconstruction through an estimate of the metric built from approximate posterior samples. If the paper is right, users can get distribution-free guarantees on PSNR, SSIM, LPIPS, or DISTS without ever seeing the true image, and can decide when to trust a reconstruction or collect more measurements.

What carries the argument

The load-bearing object is a split-conformal one-sided prediction interval. For higher-preferred metrics like PSNR and SSIM, the interval is $C_\lambda(\hat{z}) = [\hat{z} - \lambda, \infty)$, and for lower-preferred metrics like LPIPS and DISTS it is $(-\infty, \hat{z} + \lambda]$. Calibration chooses $\lambda$ as the smallest value for which the empirical miscoverage on held-out pairs stays at or below $\alpha - (1-\alpha)/n$. The estimate $\hat{z}$ is produced by an adaptive estimator: the empirical $\alpha$-quantile (or $(1-\alpha)$-quantile) of FRIQ values $m(\hat{x}, \tilde{x})$ computed from approximate posterior samples of the true image, optionally refined by quantile regression. These posterior-derived estimates make the bound respond to the test measurement and reconstruction.

What would settle it

Calibrate the quantile bound on center knee slices at acceleration $R=8$ and evaluate it on edge slices from the same volumes; the paper's own experiment shows coverage for PSNR and LPIPS dropping below $1-\alpha$ as the slice location increases. Any deployment in which a shifted test set produces empirical coverage clearly below the promised $1-\alpha$ would falsify the practical claim that the bound holds in that setting.

Watch

Extended reading notes

Core claim

The paper's central claim is that, for any recovery map $h$ and any full-reference metric $m$, the unknown quality $z_0 = m(\hat{x}_0, x_0)$ can be bounded with guaranteed probability without observing $x_0$. Under exchangeability of the pairs $(z_i, \hat{z}_i)$ across calibration and test, calibrating $\lambda$ from the empirical miscoverage of one-sided intervals yields $\Pr\{Z_0 \in C_{\hat{\lambda}(D_{\mathrm{cal}})}(\hat{Z}_0)\} \ge 1 - \alpha$. The guarantee is marginal, over both calibration and test randomness. The paper demonstrates the construction on denoising and accelerated MRI, including adaptive bounds built from approximate posterior samples that track the true metric far better than constant bounds.

Load-bearing premise

The load-bearing premise is that the test image-quality pair and the calibration image-quality pairs behave like draws from the same joint distribution; if the test images come from a different distribution than the calibration set, the coverage guarantee can fail.

Editorial extensions

If this is right

  • A clinician could check whether an accelerated MRI reconstruction meets a preset DISTS or PSNR threshold before relying on it; the multi-round experiments stop measurement collection at an average acceleration near 4 instead of 2.
  • The same calibration machinery works for any recovery network and any full-reference metric, so bounds can be instantiated for a metric matched to a given application.
  • Because the coverage guarantee is marginal, the bounds are suited to population-level decisions rather than per-image certainty.
  • Adaptive bounds track the true metric much more closely than constant bounds, with Pearson correlation above 0.5 and up to about 0.7 in the denoising experiments.
  • The learned quantile-regression variant adds little over the empirical-quantile variant in the tested settings, suggesting the simple quantile bound is a strong default.

Reading between the lines

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

  • Whenever calibration data can be stratified by acquisition conditions such as slice location, scanner, or field strength, calibrating per stratum or using weighted conformal methods could restore coverage under covariate shift.
  • Because the bound adapts to posterior samples, it could serve as a hallucination flag: a tight low bound on SSIM or DISTS means the reconstruction is formally far from any plausible true image under the posterior.
  • Treating the posterior sampler as a black box means any improvement in posterior fidelity, including samplers that target epistemic uncertainty, should directly tighten the quantile and regression bounds.
  • Risk-controlling prediction sets could upgrade the marginal guarantee to a calibration-set-conditional guarantee with two error rates, which would make the bound more trustworthy for individual deployment.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 3 minor

Summary. The paper proposes a conformal prediction framework for constructing one-sided bounds on full-reference image quality (FRIQ) metrics such as PSNR, SSIM, LPIPS, and DISTS in imaging inverse problems, without access to the true image. The authors introduce three variants: a non-adaptive bound that ignores the measurements, an adaptive quantile bound that summarizes approximate posterior samples of the image via an empirical quantile of posterior FRIQ values, and a regression bound trained with quantile regression on features derived from posterior samples. They prove that, under exchangeability of the FRIQ pairs, the calibration rule of Angelopoulos et al. yields marginal coverage of at least 1-α. Experiments on FFHQ denoising and accelerated multicoil fastMRI knee reconstruction, each with T=10,000 Monte Carlo trials, show empirical coverage very close to the nominal level, tighter bounds for the adaptive methods than the non-adaptive baseline, and a multi-round measurement protocol that attains higher average acceleration with adaptive bounds. The paper also includes an explicit distribution-shift study in which calibration on center knee slices is tested on increasingly peripheral slices, reporting coverage degradation for some metrics, and a limitations section that discloses the marginal nature of the guarantee.

Significance. If accepted, the paper provides a practically useful and theoretically sound method for communicating uncertainty about image quality in safety-critical imaging settings. The central coverage guarantee (Eq. 6) is a standard split-conformal result and is correctly applied: the interval family is monotone in lambda, calibration data are kept disjoint from training data, and the validity of the guarantee does not depend on the accuracy of the posterior sampler or the quantile-regression predictor. The empirical validation is unusually thorough, with 10,000 Monte Carlo trials, coverage checks across several metrics and values of c, and a deliberate stress test of the exchangeability assumption that reports honest degradation. The authors also openly state the limitation that the guarantee is marginal rather than conditional on a given test image or calibration set. These strengths, together with the released code, make the paper a solid contribution to uncertainty quantification for imaging inverse problems.

minor comments (3)
  1. [Appendix D] In the paragraph after Table 12, the sentence "This is can explained by the perception-distortion tradeoff" should read "This can be explained by the perception-distortion tradeoff."
  2. [Table 2 and Section 4.2] The acceptance empirical coverage of 0.9323 reported for the quantile method is noticeably below the nominal 0.95; since this quantity is conditional on the stopping event and no conditional guarantee is claimed, the statement that it is "very close to 1-α" could be softened or qualified to avoid overstating the result.
  3. [Section 4.1] The text refers to a "Flickr-Faces-HQ (FFHQ) validation dataset," but FFHQ does not have an official validation split; please clarify how this subset was defined.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the conformal coverage guarantee is a standard split-conformal theorem applied to a cleanly separated calibration set; self-citations are non-load-bearing tools.

full rationale

The paper's central guarantee, Eq. (6), is not an input disguised as a prediction. It is the standard split-conformal coverage statement for the scalar scores (Z_i, Zhat_i), and the paper states the required condition explicitly: 'which holds when {(Z0,Zhat0), (Z1,Zhat1), ..., (Zn,Zhatn)} are exchangeable (Angelopoulos et al., 2022a).' Calibration and training are kept separate ('the calibration data must be distinct from the data used to train h(·) or any other other model'), so the quantile estimator of Sec. 3.3 and the quantile-regression predictor of Sec. 3.4 are fixed before lambda is calibrated; any inaccuracy in f affects only tightness, not validity. The posterior sampler is explicitly approximate and the conformal step is presented as correcting that approximation ('an additive correction that accounts for the finite and approximate nature of the posterior image samples'), which is conformalized-quantile-regression logic rather than a circular reduction. Self-citations (Wen et al. 2023a CNF; Wen et al. 2024 multi-round protocol) are used as building blocks or experimental protocols, not as the source of the coverage guarantee, and the validity of Eq. (6) does not depend on those papers being correct. The distribution-shift study in Sec. 4.3 and the limitation statement disclose that exchangeability is load-bearing and can fail, which is the opposite of hiding the assumption. No load-bearing step reduces to its own inputs.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical or mathematical entities. The method relies on standard conformal prediction assumptions (exchangeability and split calibration) and uses existing approximate posterior samplers as tools. The only fitted quantities are hyperparameters of the optional regression bound, which do not affect the validity of the coverage guarantee.

free parameters (3)
  • Regularization weight gamma for regression bound = Selected by 5-fold cross-validation on the training split
    Tuned in Section 4.1 / Appendix F for the regression bound. It affects tightness of the bound but not the coverage guarantee, which holds for any gamma.
  • Spline knot locations t1, t2 for the quantile predictor = Placed at the 1/3 and 2/3 empirical quantiles of the mean training features (Appendix F)
    Data-dependent choice for the regression bound. It influences predictor accuracy and bound tightness, not the validity of conformal coverage.
  • Number of posterior samples c = c=32 for main experiments, with c=1,2,4,8,16 also tested
    A user-selected hyperparameter controlling the quantile estimate. The paper shows coverage remains nominal for all c, and tightness changes only slightly.
assumptions (3)
  • domain assumption The FRIQ pairs (Z_i, hat Z_i) are statistically exchangeable across calibration and test indices i=0 to n.
    This is the core condition for the conformal coverage guarantee (6), stated in Section 3 and discussed in Section 4.3. It is generally satisfied when the underlying (x_i, y_i) are i.i.d. and the posterior sampler's randomness is independent, but it can be violated under distribution shift.
  • standard math The calibration data are independent of the data used to train the recovery network h and the regression predictor f.
    Split conformal prediction requires the calibration set to be exchangeable with the test set and not used for training. The paper states this in Sections 2 and 3, following standard CP practice.
  • standard math The empirical miscoverage function in (2) is monotonically non-increasing in lambda, and (3) yields a valid calibration.
    This is the standard split CP calibration from Angelopoulos et al. (2022a), which requires the prediction intervals to be nested as lambda increases. The one-sided intervals in (4) satisfy this.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems." pith.science (2026). https://pith.science/paper/4CLQ7AAJ

@misc{pith2026250509528,
  author       = {Pith},
  title        = {Pith review of: Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4CLQ7AAJ}},
  note         = {Machine review of arXiv:2505.09528}
}
read the original abstract

In imaging inverse problems, we would like to know how close the recovered image is to the true image in terms of full-reference image quality (FRIQ) metrics like PSNR, SSIM, LPIPS, etc. This is especially important in safety-critical applications like medical imaging, where knowing that, say, the SSIM was poor could potentially avoid a costly misdiagnosis. But since we don't know the true image, computing FRIQ is non-trivial. In this work, we combine conformal prediction with approximate posterior sampling to construct bounds on FRIQ that are guaranteed to hold up to a user-specified error probability. We demonstrate our approach on image denoising and accelerated magnetic resonance imaging (MRI) problems. Code is available at https://github.com/jwen307/quality_uq.

Figures

Figures reproduced from arXiv: 2505.09528 by the authors.

Figure 1
Figure 1. Overview of method: Given a recovery xb0 of true image x0, approximate posterior samples {xe (j) 0 } c j=1, and a calibration set dcal, we construct a prediction interval Cbλ(dcal) [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Scatter plots show the non-adaptive (purple) and quantile (green) bounds [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Examples from the FFHQ denoising experiment. Top row: true image and low-LPIPS recovery. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: Mean conformal bound versus number of posterior samples [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Mean absolute difference between the bound and true FRIQ versus number of posterior samples c for FFHQ denoising. Validation procedure: Because the coverage guarantee (6) involves random calibration data and test data, we evaluate our methods using T Monte-Carlo trials…
Figure 6
Figure 6. Figure 6: Scatter plots show the non-adaptive (blue) and quantile (orange) bounds [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Fraction of accepted slices versus fi￾nal acceleration rate for multi-round MRI using DISTS with τ = 0.16. Error bars show standard deviation. Acceleration,R Fraction Accepted non-adaptive quantile [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 9
Figure 9. Figure 9: Examples of the multi-round MRI measurement procedure with DISTS at [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Qualitative examples of images from different slice locations. Slice location [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 12
Figure 12. Figure 12: The average empirical cover￾age across T = 10000 trials for test sets at different slice locations. All trials are calibrated with images from slice location 0 with α = 0.1, R = 8, and c = 32. slightly over-conservative for l > 0. Overall, the results demonstrate our …
Figure 13
Figure 13. Figure 13: Mean conformal bound versus the proportion of training samples for FFHQ denoising with [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]
Figure 14
Figure 14. Figure 14: Mean Pearson correlation coefficient between each conformal bound and the true FRIQ versus the [PITH_FULL_IMAGE:figures/full_fig_p023_14.png]
Figure 16
Figure 16. Figure 16: The mean absolute difference between the conformal bound and true image quality for varying 1 − α. Results are shown for LPIPS with c = 32. the case when α = 0.05, τ = 0.16, and c = 32. Following the multi-round measurement protocol described in Sec. 4.2, the reconstr…
Figure 17
Figure 17. Figure 17: Percent improvement in MCB versus number of samples [PITH_FULL_IMAGE:figures/full_fig_p024_17.png]
Figure 18
Figure 18. Figure 18: Qualitative example of the multi-round MRI experiment with DISTS at [PITH_FULL_IMAGE:figures/full_fig_p025_18.png]
Figure 19
Figure 19. Figure 19: Mean conformal bound versus acceleration [PITH_FULL_IMAGE:figures/full_fig_p027_19.png]
Figure 20
Figure 20. Figure 20: Fraction of accepted slices versus fi￾nal acceleration rate for multi-round MRI using DISTS. Both methods use a p-posterior average for the recovery with p = 4, c = 32, α = 0.05, and τ = 0.11. Error bars show standard deviation [PITH_FULL_IMAGE:figures/full_fig_p028_…
Figure 22
Figure 22. Figure 22: The average empirical cover￾age across T = 10000 trials for test sets at different slice locations. All trials are calibrated with images from slice location 0 with α = 0.1, R = 8, p = 1, and c = 32. consistency in ui = [ze (1) i , ze (2) i , . . . , ze (c) i ] ⊤ acro…
Figure 23
Figure 23. Figure 23: MRI sampling masks in k-space for each acceleration rate [PITH_FULL_IMAGE:figures/full_fig_p029_23.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

79 extracted references · 59 canonical work pages

  1. [1]

    Deep B ayesian inversion

    Jonas Adler and Ozan \"O ktem. Deep B ayesian inversion. arXiv:1811.05910, 2018

    arXiv 2018

  2. [2]

    Andersen, Joachim Dahl, and Lieven Vandenberghe

    Martin S. Andersen, Joachim Dahl, and Lieven Vandenberghe. CVXOPT , 2023. URL https://cvxopt.org/copyright.html

    work page 2023

  3. [3]

    Angelopoulos and Stephen Bates

    Anastasios N. Angelopoulos and Stephen Bates. Conformal prediction: A gentle introduction. Foundations and Trends in Machine Learning, 16 0 (4): 0 494--591, 2023. ISSN 1935-8237. doi:10.1561/2200000101

    doi:10.1561/2200000101 2023

  4. [4]

    Conformal risk control

    Anastasios N Angelopoulos, Stephen Bates, Adam Fisch, Lihua Lei, and Tal Schuster. Conformal risk control. arXiv:2208.02814, 2022 a

    arXiv 2022

  5. [5]

    Angelopoulos, Amit P

    Anastasios N. Angelopoulos, Amit P. Kohli, Stephen Bates, Michael I. Jordan, Jitendra Malik, Thayer Alshaabi, Srigokul Upadhyayula, and Yaniv Romano. Image-to-image regression with distribution-free uncertainty quantification and applications in imaging. In Proc. Intl. Conf. on Machine Learning, 2022 b . doi:10.48550/arXiv.2202.05265

    arXiv doi:10.48550/arxiv.2202.05265 2022

  6. [6]

    O ktem, and Carola-Bibiane Sch \

    Simon Arridge, Peter Maass, Ozan \"O ktem, and Carola-Bibiane Sch \"o nlieb. Solving inverse problems using data-driven models. Acta Numerica, 28: 0 1--174, June 2019

    work page 2019

  7. [7]

    Christopher R. S. Banerji, Tapabrata Chakraborti, Chris Harbron, and Ben D. MacArthur. Clinical AI tools must convey predictive uncertainty for each individual patient. Nature Medicine, 29 0 (12): 0 2996--2998, 2023. doi:10.1038/s41591-023-02562-7

    work page doi:10.1038/s41591-023-02562-7 2023

  8. [8]

    Quantifying model uncertainty in inverse problems via B ayesian deep gradient descent

    Riccardo Barbano, Chen Zhang, Simon Arridge, and Bangti Jin. Quantifying model uncertainty in inverse problems via B ayesian deep gradient descent. In Proc. IEEE Intl. Conf. on Pattern Recognition, pp.\ 1392--1399, 2021. doi:10.1109/ICPR48806.2021.9412521

    arXiv 2021

Show all 79 references
  1. [9]

    Conformal prediction beyond exchangeability

    Rina Foygel Barber, Emmanuel J Candes, Aaditya Ramdas, and Ryan J Tibshirani. Conformal prediction beyond exchangeability. Annals of Statistics, 51 0 (2): 0 816--845, 2023

    2023

  2. [10]

    Distribution-free, risk-controlling prediction sets

    Stephen Bates, Anastasios Angelopoulos, Lihua Lei, Jitendra Malik, and Michael Jordan. Distribution-free, risk-controlling prediction sets. Journal of the ACM, 68 0 (6), 2021. doi:10.1145/3478535

    2021 doi

  3. [11]

    Principal uncertainty quantification with spatial correlation for image restoration problems

    Omer Belhasin, Yaniv Romano, Daniel Freedman, Ehud Rivlin, and Michael Elad. Principal uncertainty quantification with spatial correlation for image restoration problems. IEEE Trans. on Pattern Analysis and Machine Intelligence, 46: 0 3321--3333, 2023

    2023

  4. [12]

    Applications, promises, and pitfalls of deep learning for fluorescence image reconstruction

    Chinmay Belthangady and Loic A Royer. Applications, promises, and pitfalls of deep learning for fluorescence image reconstruction. Nature Methods, 16 0 (12): 0 1215--1225, 2019

    2019

  5. [13]

    A regularized conditional GAN for posterior sampling in inverse problems

    Matthew Bendel, Rizwan Ahmad, and Philip Schniter. A regularized conditional GAN for posterior sampling in inverse problems. In Proc. Neural Information Processing Systems Conf., 2023

    2023

  6. [14]

    On hallucinations in tomographic image reconstruction

    Sayantan Bhadra, Varun A Kelkar, Frank J Brooks, and Mark A Anastasio. On hallucinations in tomographic image reconstruction. IEEE Trans. on Medical Imaging, 40 0 (11): 0 3249--3260, 2021

    2021

  7. [15]

    The perception-distortion tradeoff

    Yochai Blau and Tomer Michaeli. The perception-distortion tradeoff. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pp.\ 6228--6237, 2018

    2018

  8. [16]

    Torchmetrics, 2022

    Nicki Skafte Detlefsenand Jiri Borovec, Justus Schock, Ananya Harsh, Teddy Koker, Luca Di Liello, Daniel Stancl, Changsheng Quan, Maxim Grechkin, and William Falcon. Torchmetrics, 2022. URL https://github.com/Lightning-AI/torchmetrics

    2022

  9. [17]

    Oppenheimer, Abhishek Pandala, Juan José Quiroz Omaña, Nikitas Rontsis, Paarth Shah, Samuel St-Jean, Nicola Vitucci, Soeren Wolfers, and Fengyu Yang

    Stéphane Caron, Daniel Arnström, Suraj Bonagiri, Antoine Dechaume, Nikolai Flowers, Adam Heins, Takuma Ishikawa, Dustin Kenefake, Giacomo Mazzamuto, Donato Meoli, Brendan O'Donoghue, Adam A. Oppenheimer, Abhishek Pandala, Juan José Quiroz Omaña, Nikitas Rontsis, Paarth Shah, S...

    2024

  10. [18]

    Robust validation: C onfident predictions even when distributions shift

    Maxime Cauchois, Suyash Gupta, Alnur Ali, and John C Duchi. Robust validation: C onfident predictions even when distributions shift. Journal of the American Statistical Association, pp.\ 1--66, 2024

    2024

  11. [19]

    XGBoost: A scalable tree boosting system

    Tianqi Chen and Carlos Guestrin. XGBoost: A scalable tree boosting system. In Proc. Intl. Conf. on Knowledge Discovery and Data Mining, pp.\ 785--794, 2016

    2016

  12. [20]

    The potential dangers of artificial intelligence for radiology and radiologists

    Linda C Chu, Anima Anandkumar, Hoo Chang Shin, and Elliot K Fishman. The potential dangers of artificial intelligence for radiology and radiologists. Journal of the American College of Radiology, 17 0 (10): 0 1309--1311, 2020

    2020

  13. [21]

    Distribution matching losses can hallucinate features in medical image translation

    Joseph Paul Cohen, Margaux Luck, and Sina Honari. Distribution matching losses can hallucinate features in medical image translation. In Proc. Intl. Conf. on Medical Image Computation and Computer-Assisted Intervention, pp.\ 529--536, 2018

    2018

  14. [22]

    Image quality assessment: U nifying structure and texture similarity

    Keyan Ding, Kede Ma, Shiqi Wang, and Eero P Simoncelli. Image quality assessment: U nifying structure and texture similarity. IEEE Trans. on Pattern Analysis and Machine Intelligence, 44 0 (5): 0 2567--2581, 2020 a

    2020

  15. [23]

    Simoncelli

    Keyan Ding, Kede Ma, Shiqi Wang, and Eero P. Simoncelli. DISTS , 2020 b . URL https://github.com/dingkeyan93/DISTS

    2020

  16. [24]

    Efficient B ayesian computation by proximal M arkov chain M onte C arlo: W hen L angevin meets M oreau

    Alain Durmus, Eric Moulines, and Marcelo Pereyra. Efficient B ayesian computation by proximal M arkov chain M onte C arlo: W hen L angevin meets M oreau. SIAM Journal on Imaging Sciences, 11 0 (1): 0 473--506, 2018

    2018

  17. [25]

    Uncertainty quantification in deep MRI reconstruction

    Vineet Edupuganti, Morteza Mardani, Shreyas Vasanawala, and John Pauly. Uncertainty quantification in deep MRI reconstruction. IEEE Trans. on Medical Imaging, 40 0 (1): 0 239--250, January 2021

    2021

  18. [26]

    Uncertainty quantification for deep unrolling-based computational imaging

    Canberk Ekmekci and Mujdat Cetin. Uncertainty quantification for deep unrolling-based computational imaging. IEEE Trans. on Computational Imaging, 8: 0 1195--1209, 2022. doi:10.1109/TCI.2022.3233185

    2022

  19. [27]

    Quantifying generative model uncertainty in posterior sampling methods for computational imaging

    Canberk Ekmekci and Mujdat Cetin. Quantifying generative model uncertainty in posterior sampling methods for computational imaging. In Proc. Neural Information Processing Systems Workshop, 2023

    2023

  20. [28]

    Pytorch lightning, 2019

    William Falcon et al. Pytorch lightning, 2019. URL https://github.com/PyTorchLightning/pytorch-lightning

    2019

  21. [29]

    A Modern Approach to Probability Theory

    Bert E Fristedt and Lawrence F Gray. A Modern Approach to Probability Theory. Springer, 2013

    2013

  22. [30]

    The troublesome kernel--- O n hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems

    Nina M Gottschling, Vegard Antun, Anders C Hansen, and Ben Adcock. The troublesome kernel--- O n hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems. arXiv:2001.01258, 2023

    2001 arXiv

  23. [31]

    Physics-driven deep learning for computational magnetic resonance imaging: C ombining physics and machine learning for improved medical imaging

    Kerstin Hammernik, Thomas K \"u stner, Burhaneddin Yaman, Zhengnan Huang, Daniel Rueckert, Florian Knoll, and Mehmet Ak c akaya. Physics-driven deep learning for computational magnetic resonance imaging: C ombining physics and machine learning for improved medical imaging. IEE...

    2023

  24. [32]

    Denoising diffusion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In Proc. Neural Information Processing Systems Conf., volume 33, pp.\ 6840--6851, 2020

    2020

  25. [33]

    The promise and peril of deep learning in microscopy

    David P Hoffman, Isaac Slavitt, and Casey A Fitzpatrick. The promise and peril of deep learning in microscopy. Nature Methods, 18 0 (2): 0 131--132, 2021

    2021

  26. [34]

    Conffusion: C onfidence intervals for diffusion models

    Eliahu Horwitz and Yedid Hoshen. Conffusion: C onfidence intervals for diffusion models. arXiv.2211.09795, 2022. doi:10.48550/arXiv.2211.09795

    2022 doi arXiv

  27. [35]

    Robust compressed sensing MRI with deep generative priors

    Ajil Jalal, Marius Arvinte, Giannis Daras, Eric Price, Alex Dimakis, and Jonathan Tamir. Robust compressed sensing MRI with deep generative priors. In Proc. Neural Information Processing Systems Conf., 2021

    2021

  28. [36]

    Technical report (v1.0)--pseudo-random cartesian sampling for dynamic MRI

    Mihir Joshi, Aaron Pruitt, Chong Chen, Yingmin Liu, and Rizwan Ahmad. Technical report (v1.0)--pseudo-random cartesian sampling for dynamic MRI . arXiv:2206.03630, 2022

    2022 arXiv

  29. [37]

    Progressive growing of GAN s for improved quality, stability, and variation

    Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of GAN s for improved quality, stability, and variation. In Proc. Intl. Conf. on Learning Representations, 2018

    2018

  30. [38]

    A style-based generator architecture for generative adversarial networks

    Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pp.\ 4396--4405, 2019

    2019

  31. [39]

    Image quality assessment for magnetic resonance imaging

    Sergey Kastryulin, Jamil Zakirov, Nicola Pezzotti, and Dmitry V Dylov. Image quality assessment for magnetic resonance imaging. IEEE Access, 11: 0 14154--14168, 2023

    2023

  32. [40]

    Denoising diffusion restoration models

    Bahjat Kawar, Michael Elad, Stefano Ermon, and Jiaming Song. Denoising diffusion restoration models. In Proc. Neural Information Processing Systems Conf., 2022 a

    2022

  33. [41]

    Denoising diffusion restoration models

    Bahjat Kawar, Michael Elad, Stefano Ermon, and Jiaming Song. Denoising diffusion restoration models. Downloaded from https://github.com/bahjat-kawar/ddrm, May 2022 b

    2022

  34. [42]

    What uncertainties do we need in B ayesian deep learning for computer vision? In Proc

    Alex Kendall and Yarin Gal. What uncertainties do we need in B ayesian deep learning for computer vision? In Proc. Neural Information Processing Systems Conf., 2017

    2017

  35. [43]

    Deep-learning methods for parallel magnetic resonance imaging reconstruction: A survey of the current approaches, trends, and issues

    Florian Knoll, Kerstin Hammernik, Chi Zhang, Steen Moeller, Thomas Pock, Daniel K Sodickson, and Mehmet Akcakaya. Deep-learning methods for parallel magnetic resonance imaging reconstruction: A survey of the current approaches, trends, and issues. IEEE Signal Processing Magazi...

    2020

  36. [44]

    Regression quantiles

    Roger Koenker and Gilbert Bassett. Regression quantiles. Econometrica, 46 0 (1), 1978. doi:10.2307/1913643

    1978 doi

  37. [45]

    Conformal prediction masks: V isualizing uncertainty in medical imaging

    Gilad Kutiel, Regev Cohen, Michael Elad, Daniel Freedman, and Ehud Rivlin. Conformal prediction masks: V isualizing uncertainty in medical imaging. In Proc. Intl. Conf. on Learning Representations, 2023

    2023

  38. [46]

    Bayesian imaging using plug & play priors: W hen L angevin meets T weedie

    R \'e mi Laumont, Valentin De Bortoli, Andr \'e s Almansa, Julie Delon, Alain Durmus, and Marcelo Pereyra. Bayesian imaging using plug & play priors: W hen L angevin meets T weedie. SIAM Journal on Imaging Sciences, 15 0 (2): 0 701--737, 2022

    2022

  39. [47]

    Distribution-free prediction bands for non-parametric regression

    Jing Lei and Larry Wasserman. Distribution-free prediction bands for non-parametric regression. Journal of the Royal Statistical Society, 76, 2014. doi:10.1111/rssb.12021

    2014 doi

  40. [48]

    Tibshirani, and Larry Wasserman

    Jing Lei, Max G'Sell, Alessandro Rinaldo, Ryan J. Tibshirani, and Larry Wasserman. Distribution-free predictive inference for regression. Journal of the American Statistical Association, 2018

    2018

  41. [49]

    Perceptual visual quality metrics: A survey

    Weisi Lin and C-C Jay Kuo. Perceptual visual quality metrics: A survey. Journal of Visual Communication and Image Representation, 22 0 (4): 0 297--312, 2011

    2011

  42. [50]

    Convolutional neural networks as a model of the visual system: P ast, present, and future

    Grace W Lindsay. Convolutional neural networks as a model of the visual system: P ast, present, and future. Journal of Cognitive Neuroscience, 33 0 (10): 0 2017--2031, 2021

    2017

  43. [51]

    Results of the 2020 fastMRI challenge for machine learning MR image reconstruction

    Matthew J Muckley, Bruno Riemenschneider, Alireza Radmanesh, Sunwoo Kim, Geunu Jeong, Jingyu Ko, Yohan Jun, Hyungseob Shin, Dosik Hwang, Mahmoud Mostapha, et al. Results of the 2020 fastMRI challenge for machine learning MR image reconstruction. IEEE Trans. on Medical Imaging,...

    2020

  44. [52]

    Bayesian uncertainty estimation of learned variational MRI reconstruction

    Dominik Narnhofer, Alexander Effland, Erich Kobler, Kerstin Hammernik, Florian Knoll, and Thomas Pock. Bayesian uncertainty estimation of learned variational MRI reconstruction. IEEE Trans. on Medical Imaging, 41 0 (2): 0 279--291, 2022

    2022

  45. [53]

    Posterior-variance-based error quantification for inverse problems in imaging

    Dominik Narnhofer, Andreas Habring, Martin Holler, and Thomas Pock. Posterior-variance-based error quantification for inverse problems in imaging. SIAM Journal on Imaging Sciences, 17 0 (1): 0 301--333, 2024

    2024

  46. [54]

    Inductive confidence machines for regression

    Harris Papadopoulos, Kostas Proedrou, Volodya Vovk, and Alex Gammerman. Inductive confidence machines for regression. In Proc. European Conf. on Machine Learning, pp.\ 345--356, 2002. doi:10.1007/3-540-36755-1_29

    2002 doi

  47. [55]

    PyTorch: A n imperative style, high-performance deep learning library

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu ...

    2019

  48. [56]

    The NMR phased array

    Peter B Roemer, William A Edelstein, Cecil E Hayes, Steven P Souza, and Otward M Mueller. The NMR phased array. Magnetic Resonance in Medicine, 16 0 (2): 0 192--225, 1990

    1990

  49. [57]

    Cand \`e s

    Yaniv Romano, Evan Patterson, and Emmanuel J. Cand \`e s. Conformalized quantile regression. In Proc. Neural Information Processing Systems Conf., pp.\ 3543--3553, 2019. doi:10.48550/arXiv.1905.03222

    2019 doi arXiv

  50. [58]

    Angelopoulos, Stephen Bates, Yaniv Romano, and Phillip Isola

    Swami Sankaranarayanan, Anastasios N. Angelopoulos, Stephen Bates, Yaniv Romano, and Phillip Isola. Semantic uncertainty intervals for disentangled latent spaces. In Proc. Neural Information Processing Systems Conf., 2022. doi:10.48550/arXiv.2207.10074

    2022 doi arXiv

  51. [59]

    Lawrence Zitnick, Nafissa Yakubova, Florian Knoll, and Patricia Johnson

    Anuroop Sriram, Jure Zbontar, Tullie Murrell, Aaron Defazio, C. Lawrence Zitnick, Nafissa Yakubova, Florian Knoll, and Patricia Johnson. End-to-end variational networks for accelerated MRI reconstruction. In Proc. Intl. Conf. on Medical Image Computation and Computer-Assisted ...

    2020

  52. [60]

    Lawrence Zitnick, Nafissa Yakubova, Florian Knoll, and Patricia Johnson

    Anuroop Sriram, Jure Zbontar, Tullie Murrell, Aaron Defazio, C. Lawrence Zitnick, Nafissa Yakubova, Florian Knoll, and Patricia Johnson. End-to-end variational networks for accelerated MRI reconstruction. https://github.com/facebookresearch/fastMRI, 2020 b

    2020

  53. [61]

    Generative flows with invertible attentions

    Rhea Sanjay Sukthanker, Zhiwu Huang, Suryansh Kumar, Radu Timofte, and Luc Van Gool. Generative flows with invertible attentions. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, 2022. doi:10.48550/arXiv.2106.03959

    2022 doi arXiv

  54. [62]

    Deep probabilistic imaging: U ncertainty quantification and multi-modal solution characterization for computational imaging

    He Sun and Katherine L Bouman. Deep probabilistic imaging: U ncertainty quantification and multi-modal solution characterization for computational imaging. In Proc. AAAI Conf. Artificial Intelligence, volume 35, pp.\ 2628--2637, 2021

    2021

  55. [63]

    Webster Stayman, and Jeremias Sulam

    Jacopo Teneggi, Matthew Tivnan, J. Webster Stayman, and Jeremias Sulam. How to trust your diffusion model: A convex optimization approach to conformal risk control, 2023

    2023

  56. [64]

    Conformal prediction under covariate shift

    Ryan J Tibshirani, Rina Foygel Barber, Emmanuel Candes, and Aaditya Ramdas. Conformal prediction under covariate shift. In Proc. Neural Information Processing Systems Conf., volume 32, 2019

    2019

  57. [65]

    Hallucination index: A n image quality metric for generative reconstruction models

    Matthew Tivnan, Siyeop Yoon, Zhennong Chen, Xiang Li, Dufan Wu, and Quanzheng Li. Hallucination index: A n image quality metric for generative reconstruction models. In Proc. Intl. Conf. on Medical Image Computation and Computer-Assisted Intervention, pp.\ 449--458, 2024

    2024

  58. [66]

    Variational inference for computational imaging inverse problems

    Francesco Tonolini, Jack Radford, Alex Turpin, Daniele Faccio, and Roderick Murray-Smith. Variational inference for computational imaging inverse problems. Journal of Machine Learning Research, 21 0 (179): 0 1--46, 2020

    2020

  59. [67]

    Algorithmic Learning in a Random World

    Vladimir Vovk, Alexander Gammerman, and Glenn Shafer. Algorithmic Learning in a Random World. Springer, New York, 2005

    2005

  60. [68]

    Applications of objective image quality assessment methods

    Zhou Wang. Applications of objective image quality assessment methods. IEEE Signal Processing Magazine, 28 0 (6): 0 137--142, 2011

    2011

  61. [69]

    Image quality assessment: F rom error visibility to structural similarity

    Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: F rom error visibility to structural similarity. IEEE Trans. on Image Processing, 13 0 (4): 0 600--612, April 2004

    2004

  62. [70]

    A conditional normalizing flow for accelerated multi-coil MR imaging

    Jeffrey Wen, Rizwan Ahmad, and Philip Schniter. A conditional normalizing flow for accelerated multi-coil MR imaging. In Proc. Intl. Conf. on Machine Learning, 2023 a

    2023

  63. [71]

    MRI CNF , 2023 b

    Jeffrey Wen, Rizwan Ahmad, and Philip Schniter. MRI CNF , 2023 b . URL https://github.com/jwen307/mri_cnf

    2023

  64. [72]

    Task-driven uncertainty quantification in inverse problems via conformal prediction

    Jeffrey Wen, Rizwan Ahmad, and Philip Schniter. Task-driven uncertainty quantification in inverse problems via conformal prediction. arXiv:2405.18527, 2024

    2024 arXiv

  65. [73]

    Principled probabilistic imaging using diffusion models as plug-and-play priors

    Zihui Wu, Yu Sun, Yifan Chen, Bingliang Zhang, Yisong Yue, and Katherine L Bouman. Principled probabilistic imaging using diffusion models as plug-and-play priors. arXiv:2405.18782, 2024

    2024 arXiv

  66. [74]

    Reliable deep-learning-based phase imaging with uncertainty quantification

    Yujia Xue, Shiyi Cheng, Yunzhe Li, and Lei Tian. Reliable deep-learning-based phase imaging with uncertainty quantification. Optica, 6 0 (5), 2019. ISSN 2334-2536. doi:10.1364/OPTICA.6.000618

    2019 doi

  67. [75]

    Using goal-driven deep learning models to understand sensory cortex

    Daniel LK Yamins and James J DiCarlo. Using goal-driven deep learning models to understand sensory cortex. Nature neuroscience, 19 0 (3): 0 356--365, 2016

    2016

  68. [76]

    Stable deep MRI reconstruction using generative priors

    Martin Zach, Florian Knoll, and Thomas Pock. Stable deep MRI reconstruction using generative priors. IEEE Trans. on Medical Imaging, 2023

    2023

  69. [77]

    Muckley, Mary Bruno, Aaron Defazio, Marc Parente, Krzysztof J

    Jure Zbontar, Florian Knoll, Anuroop Sriram, Matthew J. Muckley, Mary Bruno, Aaron Defazio, Marc Parente, Krzysztof J. Geras, Joe Katsnelson, Hersh Chandarana, Zizhao Zhang, Michal Drozdzal, Adriana Romero, Michael Rabbat, Pascal Vincent, James Pinkerton, Duo Wang, Nafissa Yak...

    2018 arXiv

  70. [78]

    The unreasonable effectiveness of deep features as a perceptual metric

    Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pp.\ 586--595, 2018

    2018

  71. [79]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.