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REVIEW 5 major objections 5 minor 44 references

Fast Equivariant Imaging: Accelerating Unsupervised Learning and Model Adaptation via Inexact Splitting

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read By dropping the equivariance gradient from the latent update, Fast Equivariant Imaging trains unsupervised reconstruction networks roughly ten times faster than standard EI, with better generalization, and speeds up test-time adaptation.

desk verdict A credible empirical acceleration scheme for equivariant imaging, but the '10x' claim needs sharper definition and code release; the surrogate-objective concern is real but not fatal. read the letter →

arxiv 2507.06764 v5 pith:ZANEGK4C submitted 2025-07-09 eess.IV cs.CVcs.LGmath.OC

Guixian Xu , Jinglai Li , Junqi Tang This is my paper · ORCID
classification eess.IVcs.CVcs.LGmath.OC
keywords unsupervisedlearningequivariantimagingvariablesplittinginexactoptimizationinverseproblemssparse-viewCTimageinpaintingtest-timeadaptation
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

Equivariant Imaging (EI) trains reconstruction networks without ground truth by enforcing consistency under geometric transformations, but each iteration is slow because the equivariance gradient must be backpropagated through the network while refining the reconstructed image. This paper proposes Fast Equivariant Imaging (FEI), which splits that single slow problem into two alternating steps: a latent-reconstruction step that only enforces measurement consistency and proximity to the network's current output, and a pseudo-supervision step that enforces equivariance on the network weights. The paper shows numerically that this split trains a U-Net for sparse-view CT and image inpainting about ten times faster than standard EI, with equal or better PSNR and SSIM on held-out test images. It also reports that the same alternating scheme adapts a pretrained model to individual test samples under noise and distribution shifts more effectively than existing adaptation baselines. A plug-and-play variant, PnP-FEI, inserts a pretrained denoiser into the latent step so that both image-domain and measurement-domain priors contribute to unsupervised training.

What carries the argument

The load-bearing mechanism is the inexact variable-splitting reformulation of the EI objective $L_{\lambda,\alpha}(u,\theta) = f_{\mathrm{mc}}(Au,y) + \tfrac{\lambda}{2}\Vert u - F_\theta(y)\Vert^2 + \alpha\Vert T_g u - F_\theta(A T_g u)\Vert^2$. FEI alternates a latent-reconstruction step that approximately minimizes only the first two terms (using an accelerated gradient in Option 1 or one linearized gradient step in the ADMM-inspired Option 2, optionally followed by a plug-and-play denoiser in PnP-FEI), and a pseudo-supervision step that updates $\theta$ with one adaptive-gradient step on the full objective including the equivariance term. Proposition 1 is the identity that carries the argument: the gradient omitted from the $u$-update equals the gradient of the equivariance term, and its norm is controlled by the equivariance residual that the $\theta$-step reduces. This turns what would otherwise be an unjustified relaxation into a residual-controlled inexact block-coordinate scheme.

What would settle it

Compute the ratio of the omitted equivariance gradient norm to the equivariance residual norm during FEI training; Proposition 1 predicts it stays bounded by $2\alpha(1+\Vert A\Vert C_x)$. If training reaches high reconstruction quality while the ratio exceeds that bound by a large margin, the residual-control premise is violated, indicating the method succeeds for reasons other than the paper's stated mechanism.

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Extended reading notes

Core claim

The central claim is that the EI objective can be reformulated as an inexact variable-splitting problem and solved by alternating updates in which the equivariance term is deliberately excluded from the latent-image update. The paper proves (Proposition 1) that the resulting omitted-gradient error is bounded by the equivariance residual itself, $\Vert \nabla_u \Psi(u,\theta)\Vert_2 \le 2\alpha \Vert T_g\Vert (1+\Vert A\Vert C_x)\, \Vert T_g u - F_\theta(A T_g u)\Vert_2$, so the relaxation is controlled by exactly the quantity the pseudo-supervision step minimizes. On this basis the authors claim, and demonstrate in experiments on sparse-view CT and inpainting, that FEI achieves an order-of-magnitude acceleration over standard EI while improving generalization, and that the same scheme gives efficient test-time adaptation to individual samples under mixed Poisson-Gaussian noise and across anatomy, dataset, and view-ratio shifts.

Load-bearing premise

The method's success rests on the unproven assumption that the FEI alternating updates, which omit the equivariance term from the latent reconstruction step, converge to solutions as good as exact EI; Proposition 1 only bounds the size of the omitted gradient by the equivariance residual and does not establish convergence or stationarity.

Editorial extensions

If this is right

  • Training a U-Net for sparse-view CT and image inpainting without ground truth reaches competitive PSNR and SSIM roughly ten times faster than standard EI, measured in both wall-clock time and iterations.
  • Networks trained by FEI generalize better to held-out test images than those trained by EI, closing most of the gap to supervised training while using no ground-truth data.
  • FEI enables fast test-time adaptation: a pretrained EI model can be fine-tuned per test sample under unknown Poisson-Gaussian noise and across anatomy, dataset, and view-ratio shifts, outperforming MC-only, EI, and AdaptNet adaptation baselines.
  • Because the splitting decouples the latent step from the network, pretrained denoisers can be inserted as image-domain priors, combining primal- and measurement-domain information in unsupervised training.
  • The same algorithmic structure extends naturally to other EI variants such as REI, MOI, and SkEI, so the acceleration is not tied to the specific EI objective tested here.

Reading between the lines

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

  • Inference: If the tenfold acceleration transfers to larger architectures and higher-resolution volumes, EI-based unsupervised training becomes a practical alternative to supervised pretraining in medical imaging, where ground truth is scarce; the paper hints at this but does not test it.
  • Inference: Proposition 1 suggests a monitoring tool the authors do not exploit: tracking the equivariance residual during training could serve as a stopping criterion or as a schedule for the penalty parameter $\lambda$, since that residual bounds the error of the relaxed update.
  • Inference: The convergence theory gap means the method's success currently rests on empirical evidence; a natural stress test is whether the acceleration persists when the equivariance assumption is violated, such as when the test distribution lacks the assumed symmetries.
  • Inference: PnP-FEI points to a broader recipe: any prior realizable as a proximal operator can be composed with equivariance regularization in the latent step, potentially allowing task-specific priors without retraining the reconstruction network.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper proposes Fast Equivariant Imaging (FEI), an unsupervised training framework for deep imaging networks that reformulates the Equivariant Imaging (EI) objective via inexact variable splitting. FEI alternates between a latent-reconstruction step that enforces measurement consistency (and optionally a denoiser prior) and a pseudo-supervision step that updates network parameters with an equivariance loss. Two algorithmic variants are given (HQS-inspired and linearized ADMM-inspired), along with a plug-and-play extension (PnP-FEI). The central claims are that FEI achieves an order-of-magnitude acceleration over standard EI for U-Net training on sparse-view CT and image inpainting, with improved generalization, and that it enables efficient test-time adaptation. Proposition 1 bounds the gradient omitted in the latent step by the equivariance residual; the rest of the support is empirical, with experiments on CT and inpainting and adaptation studies under distribution shift.

Significance. If the empirical claims hold, FEI would make unsupervised EI training substantially more practical for high-dimensional imaging and would introduce a useful test-time adaptation tool. The algorithmic idea of decoupling equivariance from the latent update is simple and potentially extendable to EI variants (REI, MOI, SkEI). The paper is honest about the lack of a convergence result for the practical schemes, and Proposition 1 is a correct, if limited, step. However, the paper's central contribution is empirical, and the current experimental presentation does not yet establish the claimed acceleration or generalization improvement with statistical rigor. The absence of code and data further limits verification.

major comments (5)
  1. [Sec. 4.1–4.3, Eqs. (8)–(22)] The claim that FEI accelerates EI is not supported by Proposition 1. The latent-reconstruction step (e.g., Eq. (22)) minimizes only Φ(u,θ), omitting the equivariance term Ψ(u,θ). Proposition 1 bounds the norm of the omitted gradient by a constant times the equivariance residual, but it does not show that the relaxed u-update decreases the full Lagrangian L_{λ,α} in Eq. (8), nor that the iterations approach a stationary point of the EI objective. Moreover, the reformulation in Eqs. (18)–(19) is equivalent to EI only in the limit λ→∞ (i.e., u=F_θ(y) enforced exactly), whereas the experiments fix λ=1 (CT) and λ=0.1 (inpainting). Thus the observed 10x speedup may reflect optimization of a different surrogate objective rather than accelerated EI. The paper should either provide a convergence or stationarity result for the relaxed scheme, or add an experiment that isolates the surrogate effect (e.g., comparing FEI against EI at equal numbers of network evaluations on the same objective value).
  2. [Sec. 5, Figs. 2 and 4] The central '10x acceleration' claim is not precisely quantified. The paper reports PSNR and MSE curves versus iteration and wall-clock time, but does not define 'time-to-target' (e.g., time to reach a specific PSNR threshold), nor provide error bars, confidence intervals, or statistical tests on the curves. Since FEI and EI have different per-iteration costs and the curves may cross at different thresholds, the order-of-magnitude claim requires a controlled comparison with a defined target and multiple random seeds. The manuscript should specify the target metric, report mean and variance across seeds, and state the hardware and implementation details for the timing comparison.
  3. [Sec. 5.1–5.2, Tables 2 and 3] The claim of 'improved generalization performance' is not statistically established. The test set consists of only 10 images, and the reported PSNR/SSIM differences are small relative to the standard deviations (e.g., Table 2: EI 35.03±1.53 vs FEI-O1 36.17±1.44; Table 3: EI 21.49±2.30 vs FEI-O1 22.75±2.22). Without paired significance tests (e.g., Wilcoxon signed-rank or paired t-test) or a larger test set, the observed differences could be within noise. The authors should either provide such tests or moderate the generalization claim.
  4. [Sec. 4.4 and Sec. 5 (PnP-FEI)] PnP-FEI is presented as a core contribution ('the first paradigm which utilizes both the primal domain and the dual domain prior'), but the paper explicitly disclaims any convergence result for the practical pretrained-denoiser update (Sec. 4.4). Given the empirical nature of the contribution, the manuscript should at least report the sensitivity of PnP-FEI to the denoiser strength σ and to the choice of denoiser, and provide a stability discussion. Currently the PnP-FEI results in Tables 2 and 3 are not accompanied by any ablation or parameter study, which weakens the support for the 'first paradigm' claim.
  5. [General (reproducibility)] The paper does not release code or data, and the experimental section does not specify the number of random seeds, the exact hardware, or the full hyperparameter schedules (e.g., learning rate decay, early stopping criteria) beyond brief statements. Since the central contribution is empirical, this level of detail is insufficient for reproducibility. The authors should make the training and evaluation code publicly available, or at least provide a detailed appendix with all configurations and per-seed results.
minor comments (5)
  1. [Abstract and Sec. 1] There are several typos and style issues, e.g., 'Sepcifically' (Sec. 1), 'bulid' (Sec. 5(b)), 'T raining' (Sec. 5(e)), and 'a plug-and-play denoiser, this novel' (Abstract) is a comma splice. The paper would benefit from proofreading.
  2. [Fig. 1] Figure 1 introduces the EQUIV metric before it is defined in Sec. 5(a); please define it in the caption or move the definition earlier.
  3. [Algorithms 1–3] The notation for the dual variable L in Algorithm 2 is unclear: L is introduced as a vector but line 6 uses L^(y)_k without a formal definition of the per-sample dual variable. Please clarify the indexing and update rule for the dual variable.
  4. [Sec. 4.1, Eq. (13)] Equation (13) is written as ∇_uΦ(u^k,θ^k) = ∇_uL_{λ,α}(u^k,θ^k) − e_u^k, which is correct only if e_u^k is defined as ∇_uΨ(u^k,θ^k). This is indeed the definition given in Eq. (14), but the sign convention could be made more explicit to avoid confusion.
  5. [References] Reference [41] (Sun et al. for the moving average technique) is cited in Sec. 5(e) but the reference list entry appears as 'A plug-and-play deep image prior' (ICASSP 2021) which may not be the intended source for moving-average smoothing; please verify and correct.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: FEI's acceleration claim is an empirical comparison, and its theoretical content is an explicitly motivational residual bound rather than a derivation forced by its own definitions.

full rationale

The paper's central claim, an order-of-magnitude acceleration over standard Equivariant Imaging, is an empirical observation from training curves, not a quantity derived from fitted parameters or from the paper's own equations. The FEI reformulation in Eqs. (18)-(19) is a variable-splitting rewrite of the external EI objective from Chen et al. [6], and the relaxed u-update is explicitly identified as inexact. Proposition 1 bounds the omitted-gradient error by the equivariance residual, but this is a genuine mathematical inequality establishing consistency of the relaxation; it does not define the training outcome as the bound, nor does it presuppose the acceleration result. The latent-reconstruction step's use of F_theta(y) as a reference is the standard self-supervised structure of EI/FEI, and the network is subsequently evaluated on held-out test data, so no fitted parameter is renamed as a prediction. The only self-citation, to the authors' Sketched EI [17], appears in remarks about possible extensions and is not load-bearing for the main claim. The paper also explicitly limits its theoretical scope: Section 4.1 states the inexact-splitting viewpoint is used 'only to motivate' the scheme, and Section 4.4 disclaims a separate convergence result for PnP-FEI. These are honest limitations, not circular steps. Overall, the derivation chain is self-contained with respect to the acceleration claim, and no circularity is present.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The method rests on standard self-supervised and plug-and-play assumptions plus several hand-tuned hyperparameters. There are no invented physical entities. The main unstated burden is the empirical convergence of the inexact alternating scheme.

free parameters (6)
  • lambda (penalty parameter) = 1 (CT), 0.1 (inpainting)
    Controls the strength of the coupling between the latent variable and the network output; hand-tuned per task in Section 5(d).
  • alpha (equivariance strength) = 1000 (CT), 1.0 (inpainting)
    Balances the equivariance regularization; hand-tuned in Section 5(e).
  • beta (NAG momentum) = 0.1 (CT), 0.9 (inpainting)
    Momentum for the latent reconstruction solver; hand-tuned in Section 5(d).
  • eta (NAG step size) = 0.01 (CT), 0.09 (inpainting)
    Step size for latent reconstruction; hand-tuned in Section 5(d).
  • J (inner iterations) = 10
    Number of NAG or gradient iterations per latent update; set in Section 5(d).
  • gamma (ADMM latent step size) = unspecified
    Gradient step size in Algorithm 2; no numerical value is reported in the text.
assumptions (5)
  • domain assumption The clean image distribution is invariant under the chosen transformation group (rotations for CT, shifts for inpainting).
    Invoked in Section 3.2 Eq. (4) to justify the equivariance objective; if the symmetry is wrong for the data, EI and FEI lose their main signal.
  • domain assumption The forward operator A is known and the measurement model y is approximately Ax is accurate.
    Used in the measurement consistency term f_mc(Au,y) throughout Section 4; errors in the operator model would make the latent reconstruction step unreliable.
  • standard math The network F_theta is differentiable with bounded Jacobian with respect to its input.
    Assumed in Proposition 1 (Appendix A) to bound the omitted gradient; ReLU networks are only piecewise differentiable, so the bound should be understood almost everywhere.
  • ad hoc to paper The relaxed alternating scheme converges to a good solution in practice.
    Section 4.1 states the inexact splitting viewpoint is used 'only to motivate' the scheme; no convergence theorem for FEI is provided, so the training success is an empirical assumption.
  • domain assumption A pretrained denoiser provides a useful image-domain prior.
    PnP-FEI (Section 4.4) relies on this for the plug-and-play latent step; the paper does not analyze how the choice of denoiser or noise level sigma affects the result.

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Cite this review

Pith. "Pith review of Fast Equivariant Imaging: Accelerating Unsupervised Learning and Model Adaptation via Inexact Splitting." pith.science (2026). https://pith.science/paper/ZANEGK4C

@misc{pith2026250706764,
  author       = {Pith},
  title        = {Pith review of: Fast Equivariant Imaging: Accelerating Unsupervised Learning and Model Adaptation via Inexact Splitting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZANEGK4C}},
  note         = {Machine review of arXiv:2507.06764}
}
read the original abstract

In this work, we propose Fast Equivariant Imaging (FEI), a novel unsupervised learning framework to rapidly and efficiently train deep imaging networks without ground-truth data. FEI reformulates the EI objective through an inexact variable-splitting scheme, decoupling network training from an auxiliary restoration step implemented with a plug-and-play denoiser, this novel unsupervised scheme shows superior efficiency and performance compared to the standard Equivariant Imaging paradigm. In particular, our FEI schemes achieve an order-of-magnitude (10x) acceleration over standard EI on training U-Net for X-ray CT reconstruction and image inpainting, with improved generalization performance. Beyond offline training, the proposed scheme also enables efficient test-time adaptation of a pretrained model to individual samples, to secure further performance improvements. Extensive experiments show that the proposed approach provides a noticeable efficiency and performance gain over existing unsupervised methods and model adaptation techniques.

Figures

Figures reproduced from arXiv: 2507.06764 by the authors.

Figure 1
Figure 1. Evolution of the EQUIV metric during the early stages of training [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. PSNR and MSE curves with respect to iteration and time for [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 5
Figure 5. Visualization of test sample for imaging inpainting. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: PSNR and MSE curves with respect to iteration and time for im [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 6
Figure 6. Figure 6: PSNR curves vs. iteration numbers and time during adaptation [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Visualization results of different adaptation approaches across three domain shift scenarios. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

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Reference graph

Works this paper leans on

44 extracted references · 40 canonical work pages

  1. [1]

    Maximal sparsity with deep networks?

    B. Xin, Y. Wang, W. Gao, D. Wipf, and B. Wang, “Maximal sparsity with deep networks?”Advances in Neural Information Processing Systems, vol. 29, 2016

    work page 2016

  2. [2]

    Ista-net: Interpretable optimization- inspired deep network for image compressive sensing,

    J. Zhang and B. Ghanem, “Ista-net: Interpretable optimization- inspired deep network for image compressive sensing,” inProceed- ings of the IEEE conference on computer vision and pattern recognition, 2018, pp. 1828–1837

    work page 2018

  3. [3]

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

    C. Belthangady and L. A. Royer, “Applications, promises, and pitfalls of deep learning for fluorescence image reconstruction,” Nature methods, vol. 16, no. 12, pp. 1215–1225, 2019

    work page 2019

  4. [4]

    Deep image prior,

    D. Ulyanov, A. Vedaldi, and V . Lempitsky, “Deep image prior,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018, pp. 9446–9454

    2018

  5. [5]

    Dual-domain self-supervised learning and model adaption for deep compressive imaging,

    Y. Quan, X. Qin, T. Pang, and H. Ji, “Dual-domain self-supervised learning and model adaption for deep compressive imaging,” in European Conference on Computer Vision. Springer, 2022, pp. 409– 426

    work page 2022

  6. [6]

    Equivariant imaging: Learning beyond the range space,

    D. Chen, J. Tachella, and M. E. Davies, “Equivariant imaging: Learning beyond the range space,” inProceedings of the IEEE/CVF International Conference on Computer Vision, 2021, pp. 4379–4388

    2021

  7. [7]

    Robust equivariant imaging: a fully unsupervised frame- work for learning to image from noisy and partial measurements,

    ——, “Robust equivariant imaging: a fully unsupervised frame- work for learning to image from noisy and partial measurements,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022, pp. 5647–5656

    work page 2022

  8. [8]

    Test-time fast adaptation for dynamic scene deblurring via meta-auxiliary learning,

    Z. Chi, Y. Wang, Y. Yu, and J. Tang, “Test-time fast adaptation for dynamic scene deblurring via meta-auxiliary learning,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2021, pp. 9137–9146

    work page 2021

Show all 44 references
  1. [9]

    Fast adaptation to super-resolution networks via meta-learning,

    S. Park, J. Yoo, D. Cho, J. Kim, and T. H. Kim, “Fast adaptation to super-resolution networks via meta-learning,” inEuropean confer- ence on computer vision. Springer, 2020, pp. 754–769

    2020

  2. [10]

    Test-time adaptation via orthogonal meta-learning for medical imaging,

    Z. Wang, Z. Lu, T. Wang, Z. Yang, H. Yu, Z. Wang, Y. Chen, J. Lu, and Y. Zhang, “Test-time adaptation via orthogonal meta-learning for medical imaging,”IEEE Transactions on Radiation and Plasma Medical Sciences, 2024

    2024

  3. [11]

    Ground-truth free meta- learning for deep compressive sampling,

    X. Qin, Y. Quan, T. Pang, and H. Ji, “Ground-truth free meta- learning for deep compressive sampling,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023, pp. 9947–9956

    2023

  4. [12]

    Test-time training can close the natural distribution shift performance gap in deep learning based compressed sensing,

    M. Z. Darestani, J. Liu, and R. Heckel, “Test-time training can close the natural distribution shift performance gap in deep learning based compressed sensing,” inInternational conference on machine learning. PMLR, 2022, pp. 4754–4776

    2022

  5. [13]

    Test-time model adaptation for image reconstruction using self-supervised adaptive layers,

    Y. Zhao, T. Zhang, and H. Ji, “Test-time model adaptation for image reconstruction using self-supervised adaptive layers,” in European Conference on Computer Vision. Springer, 2024, pp. 111– 128

    2024

  6. [14]

    Fast image recovery using variable splitting and constrained optimiza- tion,

    M. V . Afonso, J. M. Bioucas-Dias, and M. A. Figueiredo, “Fast image recovery using variable splitting and constrained optimiza- tion,”IEEE transactions on image processing, vol. 19, no. 9, pp. 2345– 2356, 2010

    2010

  7. [15]

    First-order methods of smooth convex optimization with inexact oracle,

    O. Devolder, F. Glineur, and Y. Nesterov, “First-order methods of smooth convex optimization with inexact oracle,”Mathematical Programming, vol. 146, no. 1, pp. 37–75, 2014

    2014

  8. [16]

    Unsupervised learning from incomplete measurements for inverse problems,

    J. Tachella, D. Chen, and M. Davies, “Unsupervised learning from incomplete measurements for inverse problems,”Advances in Neural Information Processing Systems, vol. 35, pp. 4983–4995, 2022

    2022

  9. [17]

    Sketched equivariant imaging regular- ization and deep internal learning for inverse problems,

    G. Xu, J. Li, and J. Tang, “Sketched equivariant imaging regular- ization and deep internal learning for inverse problems,”arXiv preprint arXiv:2411.05771, 2024

    2024

  10. [18]

    Deep unfolding network for image super-resolution,

    K. Zhang, L. V . Gool, and R. Timofte, “Deep unfolding network for image super-resolution,” inProceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2020, pp. 3217–3226

    2020

  11. [19]

    Plug-and-play admm for image restoration: Fixed-point convergence and applications,

    S. H. Chan, X. Wang, and O. A. Elgendy, “Plug-and-play admm for image restoration: Fixed-point convergence and applications,” IEEE Transactions on Computational Imaging, vol. 3, no. 1, pp. 84–98, 2016

    2016

  12. [20]

    Admm-csnet: A deep learning approach for image compressive sensing,

    Y. Yang, J. Sun, H. Li, and Z. Xu, “Admm-csnet: A deep learning approach for image compressive sensing,”IEEE transactions on pattern analysis and machine intelligence, vol. 42, no. 3, pp. 521–538, 2018

    2018

  13. [21]

    Deepred: Deep image prior powered by red,

    G. Mataev, P . Milanfar, and M. Elad, “Deepred: Deep image prior powered by red,” inProceedings of the IEEE/CVF International Conference on Computer Vision Workshops, 2019, pp. 0–0

    2019

  14. [22]

    Self- supervised deep unrolled reconstruction using regularization by denoising,

    P . Huang, C. Zhang, X. Zhang, X. Li, L. Dong, and L. Ying, “Self- supervised deep unrolled reconstruction using regularization by denoising,”IEEE transactions on medical imaging, vol. 43, no. 3, pp. 1203–1213, 2023

    2023

  15. [23]

    Perspective-equivariant imaging: an unsupervised framework for multispectral pansharpening,

    A. Wang and M. Davies, “Perspective-equivariant imaging: an unsupervised framework for multispectral pansharpening,”arXiv preprint arXiv:2403.09327, 2024

    2024 arXiv

  16. [24]

    Equivari- ant plug-and-play image reconstruction,

    M. Terris, T. Moreau, N. Pustelnik, and J. Tachella, “Equivari- ant plug-and-play image reconstruction,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024, pp. 25 255–25 264

    2024

  17. [25]

    Algorithm unrolling: Inter- pretable, efficient deep learning for signal and image processing,

    V . Monga, Y. Li, and Y. C. Eldar, “Algorithm unrolling: Inter- pretable, efficient deep learning for signal and image processing,” IEEE Signal Processing Magazine, vol. 38, no. 2, pp. 18–44, 2021

    2021

  18. [26]

    Deep unrolling networks with recurrent momentum acceleration for nonlinear inverse prob- lems,

    Q. Zhou, J. Qian, J. Tang, and J. Li, “Deep unrolling networks with recurrent momentum acceleration for nonlinear inverse prob- lems,”Inverse Problems, vol. 40, no. 5, p. 055014, 2024

    2024

  19. [27]

    Linearized augmented lagrangian and alternating direction methods for nuclear norm minimization,

    J. Yang and X. Yuan, “Linearized augmented lagrangian and alternating direction methods for nuclear norm minimization,” Mathematics of computation, vol. 82, no. 281, pp. 301–329, 2013. 12

    2013

  20. [28]

    Inexact half-quadratic opti- mization for linear inverse problems,

    M. C. Robini, F. Yang, and Y. Zhu, “Inexact half-quadratic opti- mization for linear inverse problems,”SIAM Journal on Imaging Sciences, vol. 11, no. 2, pp. 1078–1133, 2018

    2018

  21. [29]

    Inexact half-quadratic optimization for image reconstruction,

    M. Robini, Y. Zhu, X. Lv, and W. Liu, “Inexact half-quadratic optimization for image reconstruction,” in2016 IEEE International Conference on Image Processing (ICIP). IEEE, 2016, pp. 3513–3517

    2016

  22. [30]

    Proximal alternating lin- earized minimization for nonconvex and nonsmooth problems,

    J. Bolte, S. Sabach, and M. Teboulle, “Proximal alternating lin- earized minimization for nonconvex and nonsmooth problems,” Mathematical Programming, vol. 146, no. 1, pp. 459–494, 2014

    2014

  23. [31]

    Inexact block coordinate descent algorithms for nonsmooth nonconvex optimization,

    Y. Yang, M. Pesavento, Z.-Q. Luo, and B. Ottersten, “Inexact block coordinate descent algorithms for nonsmooth nonconvex optimization,”IEEE Transactions on Signal Processing, vol. 68, pp. 947–961, 2019

    2019

  24. [32]

    A method of solving a convex programming problem with convergence rate o (1/k2),

    Y. Nesterov, “A method of solving a convex programming problem with convergence rate o (1/k2),” inSoviet Mathematics Doklady, vol. 27, no. 2, 1983, pp. 372–376

    1983

  25. [33]

    Gradient methods for minimizing composite objective func- tion,

    ——, “Gradient methods for minimizing composite objective func- tion,” UCL, Tech. Rep., 2007

    2007

  26. [34]

    A guide to stochastic optimisation for large-scale inverse problems,

    M. J. Ehrhardt, Z. Kereta, J. Liang, and J. Tang, “A guide to stochastic optimisation for large-scale inverse problems,”Inverse Problems, 2025

    2025

  27. [35]

    Provably convergent plug-and-play quasi-newton methods,

    H. Y. Tan, S. Mukherjee, J. Tang, and C.-B. Sch ¨onlieb, “Provably convergent plug-and-play quasi-newton methods,”SIAM Journal on Imaging Sciences, vol. 17, no. 2, pp. 785–819, 2024

    2024

  28. [36]

    Plug-and- play priors for model based reconstruction,

    S. V . Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and- play priors for model based reconstruction,” in2013 IEEE Global Conference on Signal and Information Processing. IEEE, 2013, pp. 945–948

    2013

  29. [37]

    Image de- noising by sparse 3-d transform-domain collaborative filtering

    K. Dabov, A. Foi, V . Katkovnik, and K. Egiazarian, “Image de- noising by sparse 3-d transform-domain collaborative filtering.” IEEE transactions on image processing: a publication of the IEEE Signal Processing Society, vol. 16, no. 8, pp. 2080–2095, 2007

    2007

  30. [38]

    Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising,

    K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang, “Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising,”IEEE Transactions on Image Processing, vol. 26, no. 7, pp. 3142–3155, 2017

    2017

  31. [39]

    Truly shift-equivariant convolu- tional neural networks with adaptive polyphase upsampling,

    A. Chaman and I. Dokmani ´c, “Truly shift-equivariant convolu- tional neural networks with adaptive polyphase upsampling,” in 2021 55th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2021, pp. 1113–1120

    2021

  32. [40]

    U-net: Convolutional networks for biomedical image segmentation,

    O. Ronneberger, P . Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” inMedical Im- age Computing and Computer-Assisted Intervention – MICCAI 2015, N. Navab, J. Hornegger, W. M. Wells, and A. F. Frangi, Eds. Cham: Springer International P...

    2015

  33. [41]

    A plug-and-play deep image prior,

    Z. Sun, F. Latorre, T. Sanchez, and V . Cevher, “A plug-and-play deep image prior,” inICASSP 2021-2021 IEEE International Con- ference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2021, pp. 8103–8107

    2021

  34. [42]

    The cancer imag- ing archive (tcia): maintaining and operating a public information repository,

    K. Clark, B. Vendt, K. Smith, J. Freymann, J. Kirby, P . Koppel, S. Moore, S. Phillips, D. Maffitt, M. Pringleet al., “The cancer imag- ing archive (tcia): maintaining and operating a public information repository,”Journal of digital imaging, vol. 26, pp. 1045–1057, 2013

    2013

  35. [43]

    Single image super- resolution from transformed self-exemplars,

    J.-B. Huang, A. Singh, and N. Ahuja, “Single image super- resolution from transformed self-exemplars,” inProceedings of the IEEE conference on computer vision and pattern recognition, 2015, pp. 5197–5206

    2015

  36. [44]

    Unsure: Unknown noise level stein’s unbiased risk estimator,

    J. Tachella, M. Davies, and L. Jacques, “Unsure: Unknown noise level stein’s unbiased risk estimator,”arXiv preprint arXiv:2409.01985, 2024

    2024 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.