Pith. sign in

REVIEW 3 major objections 5 minor 69 references

Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The paper claims that proximal trajectory training makes a learned deep image restorer approximate the proximal operator of an ideal restoration regularizer, so one unrolled model handles any compression ratio while beating CR-specific…

desk verdict New PT-loss training objective with strong across-CR results, but the oracle regularizer framing and 'arbitrary CR' claim outrun the experiments. read the letter →

arxiv 2505.23180 v1 pith:L4GVT54G submitted 2025-05-29 eess.IV cs.CV

Ping Wang , Lishun Wang , Gang Qu , Xiaodong Wang , Yulun Zhang , Xin Yuan This is my paper
classification eess.IVcs.CV
keywords single-pixelimagingcompressedsensingalgorithmunrollingproximaloperatortrajectorylosshalfquadraticsplittingADMMdeepimagerestorer
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

Single-pixel cameras reconstruct images from far fewer measurements than pixels, and the compression ratio (CR) can change from shot to shot. Existing solvers face a trade-off: plug-and-play (PnP) algorithms use one pretrained denoiser and tolerate any CR, but they are slow and only moderately accurate, while unrolling networks are fast and accurate yet must be retrained for each CR. This paper tries to get both. It unrolls HQS and ADMM iterations, each step a closed-form data-fidelity update followed by a learned deep image restorer, and trains the restorer with a proximal trajectory (PT) loss. The PT loss forces every intermediate output of the unrolled network to match the iterates of an idealized proximal algorithm whose regularizer is the squared distance to the clean image, $\bar{g}(X') = \frac{1}{2}\|X' - X\|_F^2$. If the claim holds, one ProxUnroll model reconstructs images at arbitrary CRs with accuracy and speed that match or surpass CR-specific unrolling networks, closing the flexibility gap between PnP and unrolling.

What carries the argument

The load-bearing object is the proximal trajectory (PT) loss of Eq. (19), which trains the unrolled network stage-by-stage against the ideal orbit generated by the oracle proximal operator $\mathrm{Prox}_{\bar{g}}(Q) = (\mu Q + \lambda X)/(\mu + \lambda)$, where $X$ is the clean image and $\bar{g}$ is the squared-distance regularizer of Eq. (16). This is what converts a black-box unrolled network into a proximal unrolling network whose learned restorer is meant to satisfy $R_\theta \to \mathrm{Prox}_{\bar{g}}$. The architectural carrier is the deep image restorer (DIR), a four-level encoder-decoder with memory blocks that use channel cross-attention (ChanCA) to propagate features across iterations and hybrid CNN-Transformer blocks that combine shifted-window self-attention with a gated dynamic CNN using adaptive convolutions (AdaConv).

What would settle it

On a held-out image and a compression ratio not used in training, compute the ideal trajectory via Eq. (18) and compare each unrolled output $R_\theta(Q_k)$ against the closed-form oracle step $(\mu_k Q_k + \lambda_k X)/(\mu_k + \lambda_k)$; a large average gap, especially one that grows with iteration index $k$, would directly falsify the claim that $R_\theta$ approximates $\mathrm{Prox}_{\bar{g}}$. A coarser check is to iterate the trained $R_\theta \circ \mathrm{Prox}_f$ beyond the six training steps at an unseen CR: divergence, oscillation, or convergence to the wrong image would falsify the proximal-operator interpretation.

Watch

Extended reading notes

Core claim

The central discovery is that a supervised trajectory can make an unrolled network behave like a proximal algorithm. For the ideal restoration regularizer $\bar{g}(X') = \frac{1}{2}\|X' - X\|_F^2$, the proximal operator has the closed form $\mathrm{Prox}_{\bar{g}}(Q) = (\mu Q + \lambda X)/(\mu + \lambda)$, so iterating $\mathrm{Prox}_{\bar{g}} \circ \mathrm{Prox}_f$ sends any initialization to the clean image $X$. The paper proposes to generate this ideal trajectory for each training pair and to supervise each unrolled stage with the proximal trajectory loss of Eq. (19), so that the learned deep image restorer $R_\theta$ approximates $\mathrm{Prox}_{\bar{g}}$. The result, the paper argues, is a network that inherits the interpretability and step-wise convergence of a proximal algorithm while retaining the speed of unrolling, and whose single set of weights works across compression ratios because the underlying proximal operator is degradation-agnostic.

Load-bearing premise

The argument stands or falls on the assumption that a single network, trained to imitate a per-image oracle that knows the true clean image at every step, will act like one fixed restoration rule on images and compression ratios it has never seen; this premise enters at Eqs. (16)-(19) and is supported only by the experimental convergence curves of Fig. 7.

Editorial extensions

If this is right

  • A single HQS- or ADMM-ProxUnroll model, trained once with the PT loss, reconstructs images at any compression ratio in the training range without fine-tuning or retraining, matching PnP flexibility.
  • On Set11 and BSD68, the same model outperforms previous CR-specific unrolling networks such as SAUNet and HATNet in average PSNR and SSIM across CRs from 0.01 to 0.50.
  • ProxUnroll reaches those results with fewer multiply-accumulate operations, parameters, and runtime than the compared unrolling and PnP baselines at 256×256 resolution and CR 0.25.
  • Unlike MSE-trained unrolling networks, whose intermediate iterates oscillate, ProxUnroll's intermediate outputs converge stably toward the reconstruction, giving the network step-wise interpretability.
  • Because the learned DIR approximates a proximal operator, the unrolled network can be understood as a truncated proximal algorithm rather than a black box, which the paper argues explains its flexibility across CRs.

Reading between the lines

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

  • The paper does not directly test whether $R_\theta$ matches Eq. (17) on held-out images; a head-to-head comparison against the oracle step would separate genuine proximal-operator learning from CR-conditioned memorization.
  • If the trajectory-loss recipe transfers, it could make unrolled networks degradation-flexible in other inverse problems with a closed-form $\mathrm{Prox}_f$, such as deblurring, inpainting, or MRI, which the paper does not try.
  • The ablation attributes CR flexibility partly to the memory block's cross-iteration channel attention; removing that block and measuring flexibility across unseen CRs would test whether stable intermediate representations are the actual mechanism.
  • A stress test on CRs outside [0.01, 0.50], on resolutions above 512×512, or on images from a different domain would show whether the single-model flexibility is a general property or an artifact of the training distribution.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes ProxUnroll, a single-model unrolled network for single-pixel imaging that aims to combine the accuracy and speed of deep unrolling with the flexibility across compression ratios (CRs) of plug-and-play (PnP) methods. The method alternates a closed-form proximal step for the data-fidelity term with a deep image restorer (DIR), and is trained with a proposed proximal trajectory (PT) loss. The PT loss supervises the unrolled states against an "ideal" trajectory generated by the proximal operator of an explicitly defined restoration regularizer. The paper also contributes a CNN-Transformer hybrid DIR architecture with a memory block and gated dynamic convolutions. Experiments on Set11, BSD68, and real SPI data compare HQS- and ADMM-ProxUnroll against a range of single-CR unrolling networks, multi-CR networks, and PnP baselines, reporting state-of-the-art or competitive accuracy with lower computation and runtime. The central claims are that the learned DIR approximates the proximal operator of an ideal explicit regularizer, and that a single ProxUnroll model can handle arbitrary CRs like PnP algorithms.

Significance. If the central claims were fully established, this would be a practically valuable result: a single unrolled network that is simultaneously fast, accurate, and flexible over CRs would combine advantages that are currently split between PnP and unrolling methods. The paper has concrete strengths: extensive comparisons on standard benchmarks, a reproducibility-friendly release of source code and models, clear efficiency gains in MACs and runtime (Table 3), and ablation studies isolating the contribution of the proposed architecture components. The convergence curves in Fig. 7 also provide a useful empirical illustration of the difference between standard end-to-end training and trajectory-based training. However, the significance is moderated by two load-bearing issues: the theoretical interpretation of the learned network as a proximal operator of a fixed regularizer is not established (because the "ideal" regularizer depends on the ground-truth image), and the claimed flexibility over arbitrary CRs is only tested within the training CR interval. These issues are fixable in principle, but they require either a reframing of the contribution or additional experiments.

major comments (3)
  1. [§4.1, Eq. (16)–(18)] The "explicit restoration regularizer" defined in Eq. (16) as g-bar(X') = (1/2)||X' - X||_F^2 depends on the unknown clean image X. Consequently, Prox_{g-bar} in Eq. (17) is an oracle operator that knows the ground truth, not a regularizer in the standard inverse-problem sense. The statement that training R_theta with the PT loss yields R_theta → Prox_g for some fixed g (Eq. (15) and the surrounding text) is therefore not established: the training objective matches R_theta to per-image oracle trajectories, and does not by itself identify a fixed regularizer whose proximal operator R_theta approximates. This is load-bearing for the interpretability and convergence-guarantee narrative, and the paper should either provide a rigorous statement of what class of fixed g could justify the approximation, or explicitly reframe the method as trajectory matching without claiming proximal-operator interpretability.
  2. [§5.1, Table 2 and §5, training protocol] The flexibility claim "can flexibly handle arbitrary CRs with a single model like PnP algorithms" is evaluated only at CRs {0.01, 0.04, 0.10, 0.25, 0.50}, all of which lie within the training interval [0.01, 0.50] stated in the experiments section. Because the PT loss in Eq. (19) is computed using training pairs generated with CRs in this interval, the model may interpolate over these CRs rather than generalize to unseen ones. PnP baselines, by contrast, use a pretrained denoiser that never sees the SPI measurement model or CR, so their flexibility is demonstrated out-of-distribution. To support the "Arbitrary" label in Table 2 and the claimed equivalence to PnP flexibility, the authors should report results at held-out CRs not seen during training (e.g., 0.03, 0.15, 0.35, or 0.60) using the same single model.
  3. [§4.1, Eq. (19) and §5.3, Fig. 7] The text states that the PT loss endows the unrolled network with convergence guarantees or "fast convergence" towards the ground truth, and that intermediate subnets become interpretable as proximal restoration operators. However, Eq. (19) is a finite-horizon (K=6) supervised trajectory-matching objective; it does not provide a convergence guarantee for R_theta as k → ∞, nor does it formally establish that R_theta is a proximal operator. The empirical curves in Fig. 7 show stable behavior on the tested CRs, but this is an empirical observation, not a guarantee. The authors should temper the language (e.g., "empirically faster and more stable convergence") or supply a formal convergence theorem under explicit assumptions on R_theta.
minor comments (5)
  1. [Throughout] The acronym for the proposed loss is inconsistent: the abstract and §4.1 introduce "proximal trajectory (PT) loss", but Eq. (19) and §5.3 repeatedly call it "PL loss", and the conclusion says "proximal trajectory (PL) loss". Please unify the notation.
  2. [Fig. 1] The left panel of Fig. 1 has illegible axis labels in the submitted rendering (the compression-ratio axis label appears garbled). Please ensure the figure is legible in the final version.
  3. [§5.2] The text says that among the compared networks, only SAUNet and HATNet are practical for real SPI cameras, yet the experiments also report PnP-DRUNet on the real data. Please reconcile this sentence with the actual comparison set.
  4. [Table 2] The flexibility column for COAST is marked "Multiple", but the text explains that COAST is only flexible for CRs seen during its training (0.10–0.50) and degrades at CR=0.01. Marking it "Seen-CR only" would avoid the misleading impression that its flexibility is comparable to PnP or ProxUnroll.
  5. [Eq. (15)] The notation R_theta → Prox_g uses an undefined arrow. Please specify the intended notion of approximation (e.g., pointwise convergence, Lipschitz bound, or empirical trajectory matching) to make the statement precise.

Circularity Check

1 steps flagged · score 2.0 of 10

No derivationally circular step; the PT loss is a supervised objective, though the 'explicit restoration regularizer' is defined via the ground truth, making the interpretability claim self-referential.

  1. self definitional [Section 4.1, Eqs. (16)-(19)]
    "we define the squared Euclidean distance between a degraded image X′ and its clear image X as an explicit regularization function: ¯g(X′) = 1/2 ∥X′ − X∥²_F. ... Prox¯g(Q) = (µQ + λX)/(µ + λ). ... During supervised training, we use Prox¯g to guide the optimization of Rθ in Eq. (15) such that Rθ serves as an implicit image restorer to approximate Prox¯g."

    The 'explicit restoration regularizer' in Eq. (16) is defined using the ground-truth clean image X, so its proximal operator (Eq. (17)) is an oracle that already knows the target. The PT loss (Eq. (19)) then minimizes Σ ||X_{k+1} − Xbar_{k+1}||², where Xbar_{k+1} is generated by that oracle. Thus the statement that the learned DIR 'approximates the proximal operator of an ideal explicit restoration regularizer' is true by construction of the training target, not by independent derivation; the claimed convergence X_k→X is a tautology of pulling toward X. No fixed target-independent regularizer is identified, so the interpretability/flexibility story rests on this self-referential definition rather than on a derived equivalence.

full rationale

The central derivation is not circular in the sense of reusing the final result to produce the method: the PT loss is a supervised objective that explicitly trains R_theta to match an oracle trajectory, and the reported accuracy and speed are genuine empirical measurements against external baselines (SAUNet, HATNet, PnP-DRUNet, etc.). The only self-referential element is the framing of Eq. (16): the 'ideal explicit restoration regularizer' is defined per image using the ground truth, so Prox_bar_g is an oracle and the claim that R_theta approximates a proximal operator is a restatement of the training objective rather than a discovered, target-independent property. This is a soundness and interpretation concern, not a derivation-level circularity, and it does not affect the validity of the experimental comparisons. No load-bearing self-citations or imported uniqueness theorems are present, and no 'prediction' is statistically forced by a fitted parameter. The flexibility claim is only tested at CRs inside the training interval [0.01, 0.50], but that is an extrapolation/generalization gap, not circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The method rests on a few mathematical facts, such as convergence of proximal algorithms and closed-form Prox_f for row-orthogonal Phi, and two paper-specific assumptions: the oracle regularizer in Eq. (16) and the trainability of mu and lambda parameters. No new physical entities are introduced; the proposed network components are computational artifacts.

free parameters (5)
  • Proximal penalty parameters mu_k (HQS) and related mu_k in ADMM = not reported in main text
    Eq. (19) declares {mu_k} trainable in the unrolled network; these control the data-fidelity versus regularization balance at each stage.
  • Ideal-trajectory parameters {bar_mu_k, bar_lambda_k} = not reported in main text
    Eq. (19) declares them trainable; the final stage is fixed to (0,1) to force the trajectory to end at the ground truth.
  • PT loss weights alpha_k = not reported
    Eq. (19) includes alpha_k controlling per-stage proximity strength; no values or schedule are given in the main text.
  • Number of unrolled iterations K = 6
    Section 5 states the networks use 6 iterations; the choice is not justified or ablated.
  • Channel width C and block counts in DIR = not fully specified in main text
    The architecture in Fig. 4 and Section 4.2 is described, but exact widths, depths, and window sizes are not given with enough precision to reproduce without the code.
assumptions (4)
  • standard math Proximal operators of HQS and ADMM converge to stationary points of Eq. (3) for a proper regularizer g
    Invoked in Section 3.2, citing Parikh and Boyd and standard proximal splitting theory.
  • domain assumption SPI measurement matrix can be written as Kronecker product Phi = W ⊗ H with row-orthogonal factors, giving closed-form Prox_f in Eq. (11)
    Section 3.1 states this as a practical SPI camera model; it does not hold for arbitrary compressive sensing matrices but is standard for SPI with separable masks.
  • ad hoc to paper A single network R_theta trained with the PT loss approximates the per-image proximal operators Prox_{bar g} well enough to provide convergence and flexibility on unseen images and CRs
    This is the central training hypothesis; only empirical convergence curves in Fig. 7 are offered, with no theorem or bound.
  • ad hoc to paper The oracle function bar g(X') = 1/2 || X' - X ||_F^2 with X the ground truth is a legitimate explicit restoration regularizer whose proximal operator defines a meaningful target trajectory
    Eq. (16) introduces the ground-truth-dependent function as a regularizer. Standard regularizers do not depend on the unknown target, so this is an unusual modeling choice.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging." pith.science (2026). https://pith.science/paper/L4GVT54G

@misc{pith2026250523180,
  author       = {Pith},
  title        = {Pith review of: Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L4GVT54G}},
  note         = {Machine review of arXiv:2505.23180}
}
read the original abstract

Deep-unrolling and plug-and-play (PnP) approaches have become the de-facto standard solvers for single-pixel imaging (SPI) inverse problem. PnP approaches, a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep denoiser, are flexible for varying compression ratios (CRs) but are limited in reconstruction accuracy and speed. Conversely, unrolling approaches, a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network, typically achieve better accuracy with faster inference but require fine-tuning or even retraining when CR changes. In this paper, we address the challenge of integrating the strengths of both classes of solvers. To this end, we design an efficient deep image restorer (DIR) for the unrolling of HQS (half quadratic splitting) and ADMM (alternating direction method of multipliers). More importantly, a general proximal trajectory (PT) loss function is proposed to train HQS/ADMM-unrolling networks such that learned DIR approximates the proximal operator of an ideal explicit restoration regularizer. Extensive experiments demonstrate that, the resulting proximal unrolling networks can not only flexibly handle varying CRs with a single model like PnP algorithms, but also outperform previous CR-specific unrolling networks in both reconstruction accuracy and speed. Source codes and models are available at https://github.com/pwangcs/ProxUnroll.

Figures

Figures reproduced from arXiv: 2505.23180 by the authors.

Figure 1
Figure 1. Average PSNR (left) of different methods at compres [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Degradations under different compressive ratios (CRs). [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Proximal algorithm unrolling via trajectory loss. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Illustration of the proposed deep image restorer (DIR) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Visual comparisons on “barbara” from Set11 dataset at CR [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Visual comparisons on real SPI data “resolution target” reported in [ [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Convergence curves of different unrolling methods. [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

69 extracted references · 65 canonical work pages

  1. [1]

    Modl: Model-based deep learning architecture for inverse problems

    Hemant K Aggarwal, Merry P Mani, and Mathews Jacob. Modl: Model-based deep learning architecture for inverse problems. IEEE transactions on medical imaging , 38(2): 394–405, 2018. 2

    work page 2018

  2. [2]

    Contour detection and hierarchical image seg- mentation

    Pablo Arbel ´aez, Michael Maire, Charless Fowlkes, and Ji- tendra Malik. Contour detection and hierarchical image seg- mentation. IEEE Transactions on Pattern Analysis and Ma- chine Intelligence, 33(5):898–916, 2011. 6

    work page 2011

  3. [3]

    A fast iterative shrinkage- thresholding algorithm for linear inverse problems

    Amir Beck and Marc Teboulle. A fast iterative shrinkage- thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183–202, 2009. 2

    work page 2009

  4. [4]

    Deep unfolding of a proximal interior point method for image restoration

    Carla Bertocchi, Emilie Chouzenoux, Marie-Caroline Cor- bineau, Jean-Christophe Pesquet, and Marco Prato. Deep unfolding of a proximal interior point method for image restoration. Inverse Problems, 36(3):034005, 2020. 2

    work page 2020

  5. [5]

    Iterative hard thresholding for compressed sensing

    Thomas Blumensath and Mike E Davies. Iterative hard thresholding for compressed sensing. Applied and Compu- tational Harmonic Analysis, 27(3):265–274, 2009. 2

    work page 2009

  6. [6]

    Caiafa and Andrzej Cichocki

    Cesar F. Caiafa and Andrzej Cichocki. Multidimensional compressed sensing and their applications. Wiley Interdis- ciplinary Reviews: Data Mining and Knowledge Discovery , 3(6):355–380, 2013. 3

    work page 2013

  7. [7]

    Candes and Terence Tao

    Emmanuel J. Candes and Terence Tao. Near-optimal sig- nal recovery from random projections: Universal encoding strategies? IEEE Transactions on Information Theory , 52 (12):5406–5425, 2006. 1

    work page 2006

  8. [8]

    Ro- bust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information

    Emmanuel J Cand `es, Justin Romberg, and Terence Tao. Ro- bust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transac- tions on Information Theory, 52(2):489–509, 2006. 1

    work page 2006

Show all 69 references
  1. [9]

    Proxi- mal splitting methods in signal processing

    Patrick L Combettes and Jean-Christophe Pesquet. Proxi- mal splitting methods in signal processing. Fixed-point al- gorithms for inverse problems in science and engineering , pages 185–212, 2011. 1

    2011

  2. [10]

    Compressive sensing via nonlocal low-rank regu- larization

    Weisheng Dong, Guangming Shi, Xin Li, Yi Ma, and Feng Huang. Compressive sensing via nonlocal low-rank regu- larization. IEEE Transactions on Image Processing , 23(8): 3618–3632, 2014. 2

    2014

  3. [11]

    Denoising prior driven deep neural network for image restoration

    Weisheng Dong, Peiyao Wang, Wotao Yin, Guangming Shi, Fangfang Wu, and Xiaotong Lu. Denoising prior driven deep neural network for image restoration. IEEE transac- tions on pattern analysis and machine intelligence , 41(10): 2305–2318, 2018. 2

    2018

  4. [12]

    M. F. Duarte and R. G. Baraniuk. Kronecker compressive sensing. IEEE Trans Image Process, 21(2):494–504, 2012. 3

    2012

  5. [13]

    Single-pixel imaging via compressive sampling

    Marco F Duarte, Mark A Davenport, Dharmpal Takhar, Ja- son N Laska, Ting Sun, Kevin F Kelly, and Richard G Bara- niuk. Single-pixel imaging via compressive sampling. IEEE Signal Processing Magazine, 25(2):83–91, 2008. 1

    2008

  6. [14]

    Principles and prospects for single-pixel imaging

    Matthew P Edgar, Graham M Gibson, and Miles J Padgett. Principles and prospects for single-pixel imaging. Nature photonics, 13(1):13–20, 2019. 1

    2019

  7. [15]

    What’s in a prior? learned proximal networks for inverse problems

    Zhenghan Fang, Sam Buchanan, and Jeremias Sulam. What’s in a prior? learned proximal networks for inverse problems. In The Twelfth International Conference on Learning Representations. 2, 3

  8. [16]

    Gradient projection for sparse reconstruction: Ap- plication to compressed sensing and other inverse problems

    M ´ario AT Figueiredo, Robert D Nowak, and Stephen J Wright. Gradient projection for sparse reconstruction: Ap- plication to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing, 1(4): 586–597, 2007. 1, 2

    2007

  9. [17]

    Nonlinear image recov- ery with half-quadratic regularization

    Donald Geman and Chengda Yang. Nonlinear image recov- ery with half-quadratic regularization. IEEE transactions on Image Processing, 4(7):932–946, 1995. 1, 2

    1995

  10. [18]

    Cpp-net: Embracing multi- scale feature fusion into deep unfolding cp-ppa network for compressive sensing

    Zhen Guo and Hongping Gan. Cpp-net: Embracing multi- scale feature fusion into deep unfolding cp-ppa network for compressive sensing. In Proceedings of the IEEE/CVF Con- ference on Computer Vision and Pattern Recognition, pages 25086–25095, 2024. 2, 3, 6, 7, 8

    2024

  11. [19]

    Robust stochastically-descending unrolled net- works

    Samar Hadou, Navid NaderiAlizadeh, and Alejandro Ribeiro. Robust stochastically-descending unrolled net- works. IEEE Transactions on Signal Processing , 72:5484– 5499, 2024. 4, 5

    2024

  12. [20]

    Single pixel imaging at megahertz switching rates via cyclic hadamard masks

    Evgeny Hahamovich, Sagi Monin, Yoav Hazan, and Amir Rosenthal. Single pixel imaging at megahertz switching rates via cyclic hadamard masks. Nature communications, 12(1): 4516, 2021. 1

    2021

  13. [21]

    Exploiting structure in wavelet-based bayesian compressive sensing

    Lihan He and Lawrence Carin. Exploiting structure in wavelet-based bayesian compressive sensing. IEEE Trans- actions on Signal Processing, 57(9):3488–3497, 2009. 2

    2009

  14. [22]

    Stochastic deep restoration priors for imaging inverse problems

    Yuyang Hu, Albert Peng, Weijie Gan, Peyman Milanfar, Mauricio Delbracio, and Ulugbek S Kamilov. Stochastic deep restoration priors for imaging inverse problems. arXiv preprint arXiv:2410.02057, 2024. 2, 3

    2024 arXiv

  15. [23]

    Gradient step denoiser for convergent plug-and-play

    Samuel Hurault, Arthur Leclaire, and Nicolas Papadakis. Gradient step denoiser for convergent plug-and-play. In International Conference on Learning Representations (ICLR’22), 2022. 3

    2022

  16. [24]

    Proximal denoiser for convergent plug-and-play optimiza- tion with nonconvex regularization

    Samuel Hurault, Arthur Leclaire, and Nicolas Papadakis. Proximal denoiser for convergent plug-and-play optimiza- tion with nonconvex regularization. In International Confer- ence on Machine Learning, pages 9483–9505. PMLR, 2022. 2, 3

    2022

  17. [25]

    Kamilov, Charles A

    Ulugbek S. Kamilov, Charles A. Bouman, Gregery T. Buz- zard, and Brendt Wohlberg. Plug-and-play methods for inte- grating physical and learned models in computational imag- ing: Theory, algorithms, and applications. IEEE Signal Pro- cessing Magazine, 40(1):85–97, 2023. 2

    2023

  18. [26]

    Com- pressed sensing using a gaussian scale mixtures model in wavelet domain

    Yookyung Kim, Mariappan S Nadar, and Ali Bilgin. Com- pressed sensing using a gaussian scale mixtures model in wavelet domain. In Proceedings of the IEEE International Conference on Image Processing (ICIP), 2010. 2

    2010

  19. [27]

    Reconnet: Non-iterative reconstruc- tion of images from compressively sensed measurements

    Kuldeep Kulkarni, Suhas Lohit, Pavan Turaga, Ronan Ker- viche, and Amit Ashok. Reconnet: Non-iterative reconstruc- tion of images from compressively sensed measurements. In Proceedings of the IEEE/CVF Conference on Computer Vi- sion and Pattern Recognition (CVPR), pages 449–45...

    2016

  20. [28]

    An efficient algorithm for compressed mr imaging using to- tal variation and wavelets

    Shiqian Ma, Wotao Yin, Yin Zhang, and Amit Chakraborty. An efficient algorithm for compressed mr imaging using to- tal variation and wavelets. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 1–8, 2008. 2

    2008

  21. [29]

    Learned d-amp: Principled neural network based compressive image recovery

    Chris Metzler, Ali Mousavi, and Richard Baraniuk. Learned d-amp: Principled neural network based compressive image recovery. InAdvances in Neural Information Processing Sys- tems (NeurIPS), 2017. 2

    2017

  22. [30]

    From denoising to compressed sensing

    Christopher A Metzler, Arian Maleki, and Richard G Bara- niuk. From denoising to compressed sensing. IEEE Trans- actions on Information Theory, 62(9):5117–5144, 2016. 2

    2016

  23. [31]

    Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing

    Vishal Monga, Yuelong Li, and Yonina C Eldar. Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing. IEEE Signal Processing Magazine , 38(2):18–44, 2021. 2

    2021

  24. [32]

    Deep generalized unfolding networks for image restoration

    Chong Mou, Qian Wang, and Jian Zhang. Deep generalized unfolding networks for image restoration. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 17399–17410, 2022. 2, 3, 6, 7

    2022

  25. [33]

    Proximal algorithms

    Neal Parikh, Stephen Boyd, et al. Proximal algorithms. Foundations and trends® in Optimization , 1(3):127–239,

  26. [34]

    How do vision transform- ers work? In 10th International Conference on Learning Representations, ICLR 2022, 2022

    Namuk Park and Songkuk Kim. How do vision transform- ers work? In 10th International Conference on Learning Representations, ICLR 2022, 2022. 6

    2022

  27. [35]

    Dual-scale trans- former for large-scale single-pixel imaging

    Gang Qu, Ping Wang, and Xin Yuan. Dual-scale trans- former for large-scale single-pixel imaging. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pat- tern Recognition, pages 25327–25337, 2024. 2, 6, 7, 8

    2024

  28. [36]

    The little engine that could: Regularization by denoising (red)

    Yaniv Romano, Michael Elad, and Peyman Milanfar. The little engine that could: Regularization by denoising (red). SIAM Journal on Imaging Sciences, 10(4):1804–1844, 2017. 2

    2017

  29. [37]

    Plug-and-play methods provably converge with properly trained denoisers

    Ernest Ryu, Jialin Liu, Sicheng Wang, Xiaohan Chen, Zhangyang Wang, and Wotao Yin. Plug-and-play methods provably converge with properly trained denoisers. In In- ternational Conference on Machine Learning , pages 5546–

  30. [38]

    Transcs: a transformer-based hybrid architecture for image compressed sensing

    Minghe Shen, Hongping Gan, Chao Ning, Yi Hua, and Tao Zhang. Transcs: a transformer-based hybrid architecture for image compressed sensing. IEEE Transactions on Image Processing, 31:6991–7005, 2022. 2, 6, 7

    2022

  31. [39]

    Im- age compressed sensing using convolutional neural network

    Wuzhen Shi, Feng Jiang, Shaohui Liu, and Debin Zhao. Im- age compressed sensing using convolutional neural network. IEEE Transactions on Image Processing, 29:375–388, 2019. 2, 6, 7

    2019

  32. [40]

    Scalable convolutional neural network for image compressed sensing

    Wuzhen Shi, Feng Jiang, Shaohui Liu, and Debin Zhao. Scalable convolutional neural network for image compressed sensing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pages 12290–12299, 2019. 2

    2019

  33. [41]

    Memory- augmented deep unfolding network for compressive sensing

    Jiechong Song, Bin Chen, and Jian Zhang. Memory- augmented deep unfolding network for compressive sensing. In Proceedings of the 29th ACM International Conference on Multimedia, pages 4249–4258, 2021. 2, 3, 6, 7

    2021

  34. [42]

    Optimization-inspired cross-attention transformer for compressive sensing

    Jiechong Song, Chong Mou, Shiqi Wang, Siwei Ma, and Jian Zhang. Optimization-inspired cross-attention transformer for compressive sensing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 6174–6184, 2023. 2, 3, 6, 7

    2023

  35. [43]

    3d computational imaging with single-pixel detectors

    Baoqing Sun, Matthew P Edgar, Richard Bowman, Liberty E Vittert, Stuart Welsh, Adrian Bowman, and Miles J Padgett. 3d computational imaging with single-pixel detectors. Sci- ence, 340(6134):844–847, 2013. 1

    2013

  36. [44]

    Block coordi- nate regularization by denoising

    Yu Sun, Jiaming Liu, and Ulugbek Kamilov. Block coordi- nate regularization by denoising. Advances in neural infor- mation processing systems, 32, 2019. 2

    2019

  37. [45]

    Scalable plug-and-play admm with con- vergence guarantees

    Yu Sun, Zihui Wu, Xiaojian Xu, Brendt Wohlberg, and Ulug- bek S Kamilov. Scalable plug-and-play admm with con- vergence guarantees. IEEE Transactions on Computational Imaging, 7:849–863, 2021. 2

    2021

  38. [46]

    Plug-and-play algorithms for single-pixel imaging

    Ye Tian, Ying Fu, and Jun Zhang. Plug-and-play algorithms for single-pixel imaging. Optics and Lasers in Engineering, 154:106970, 2022. 2

    2022

  39. [47]

    Saunet: Spatial-attention unfold- ing network for image compressive sensing

    Ping Wang and Xin Yuan. Saunet: Spatial-attention unfold- ing network for image compressive sensing. In Proceedings of the 31st ACM International Conference on Multimedia , pages 5099–5108, 2023. 2, 3, 5, 6, 7, 8

    2023

  40. [48]

    Full- resolution and full-dynamic-range coded aperture compres- sive temporal imaging

    Ping Wang, Lishun Wang, Mu Qiao, and Xin Yuan. Full- resolution and full-dynamic-range coded aperture compres- sive temporal imaging. Optics Letters, 48(18):4813–4816,

  41. [49]

    Deep optics for video snapshot compressive imaging

    Ping Wang, Lishun Wang, and Xin Yuan. Deep optics for video snapshot compressive imaging. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 10646–10656, 2023

    2023

  42. [50]

    Hier- archical separable video transformer for snapshot compres- sive imaging

    Ping Wang, Yulun Zhang, Lishun Wang, and Xin Yuan. Hier- archical separable video transformer for snapshot compres- sive imaging. In European Conference on Computer Vision, pages 104–122. Springer, 2024. 2

    2024

  43. [51]

    Ufc-net: Unrolling fixed-point continuous network for deep compressive sens- ing

    Xiaoyang Wang and Hongping Gan. Ufc-net: Unrolling fixed-point continuous network for deep compressive sens- ing. In Proceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition , pages 25149–25159,

  44. [52]

    Terahertz compressive imaging with metamaterial spatial light modulators

    Claire M Watts, David Shrekenhamer, John Montoya, Guy Lipworth, John Hunt, Timothy Sleasman, Sanjay Krishna, David R Smith, and Willie J Padilla. Terahertz compressive imaging with metamaterial spatial light modulators. Nature photonics, 8(8):605–609, 2014. 1

    2014

  45. [53]

    Alternating direction algo- rithms for ℓ1-problems in compressive sensing

    Junfeng Yang and Yin Zhang. Alternating direction algo- rithms for ℓ1-problems in compressive sensing. SIAM Jour- nal on Scientific Computing, 33(1):250–278, 2011. 2

    2011

  46. [54]

    Admm- csnet: A deep learning approach for image compressive sens- ing

    Yan Yang, Jian Sun, Huibin Li, and Zongben Xu. Admm- csnet: A deep learning approach for image compressive sens- ing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42(3):521–538, 2018. 2

    2018

  47. [55]

    Dr2-net: Deep residual re- construction network for image compressive sensing

    Hantao Yao, Feng Dai, Shiliang Zhang, Yongdong Zhang, Qi Tian, and Changsheng Xu. Dr2-net: Deep residual re- construction network for image compressive sensing. Neu- rocomputing, 359:483–493, 2019. 2

    2019

  48. [56]

    Csformer: Bridging convolution and transformer for compressive sensing.IEEE Transactions on Image Processing, 32:2827–2842, 2023

    Dongjie Ye, Zhangkai Ni, Hanli Wang, Jian Zhang, Shiqi Wang, and Sam Kwong. Csformer: Bridging convolution and transformer for compressive sensing.IEEE Transactions on Image Processing, 32:2827–2842, 2023. 2, 3, 6, 7

    2023

  49. [57]

    Coast: Controllable arbitrary-sampling network for com- pressive sensing

    Di You, Jian Zhang, Jingfen Xie, Bin Chen, and Siwei Ma. Coast: Controllable arbitrary-sampling network for com- pressive sensing. IEEE Transactions on Image Processing , 30:6066–6080, 2021. 2, 3, 6, 7

    2021

  50. [58]

    Generalized alternating projection based total variation minimization for compressive sensing

    Xin Yuan. Generalized alternating projection based total variation minimization for compressive sensing. In 2016 IEEE International conference on image processing (ICIP) , pages 2539–2543. IEEE, 2016. 2

    2016

  51. [59]

    Brady, and Aggelos K

    Xin Yuan, David J. Brady, and Aggelos K. Katsaggelos. Snapshot compressive imaging: Theory, algorithms, and ap- plications. IEEE Signal Processing Magazine, 38(2):65–88,

  52. [60]

    Restormer: Efficient transformer for high-resolution image restoration

    Syed Waqas Zamir, Aditya Arora, Salman Khan, Mu- nawar Hayat, Fahad Shahbaz Khan, and Ming-Hsuan Yang. Restormer: Efficient transformer for high-resolution image restoration. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 572...

    2022

  53. [61]

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

    Jian Zhang and Bernard Ghanem. Ista-net: Interpretable optimization-inspired deep network for image compressive sensing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pages 1828–1837, 2018. 2, 3, 6, 7

    2018

  54. [62]

    Optimization- inspired compact deep compressive sensing.IEEE Journal of Selected Topics in Signal Processing, 14(4):765–774, 2020

    Jian Zhang, Chen Zhao, and Wen Gao. Optimization- inspired compact deep compressive sensing.IEEE Journal of Selected Topics in Signal Processing, 14(4):765–774, 2020. 2, 3, 6, 7

    2020

  55. [63]

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

    Kai Zhang, Wangmeng Zuo, Yunjin Chen, Deyu Meng, and Lei Zhang. Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising. IEEE transactions on image processing, 26(7):3142–3155, 2017. 2, 3, 6

    2017

  56. [64]

    Learning deep cnn denoiser prior for image restoration

    Kai Zhang, Wangmeng Zuo, Shuhang Gu, and Lei Zhang. Learning deep cnn denoiser prior for image restoration. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3929–3938, 2017. 2

    2017

  57. [65]

    Ffdnet: Toward a fast and flexible solution for cnn-based image denoising

    Kai Zhang, Wangmeng Zuo, and Lei Zhang. Ffdnet: Toward a fast and flexible solution for cnn-based image denoising. IEEE Transactions on Image Processing, 27(9):4608–4622,

  58. [66]

    Plug-and-play image restora- tion with deep denoiser prior

    Kai Zhang, Yawei Li, Wangmeng Zuo, Lei Zhang, Luc Van Gool, and Radu Timofte. Plug-and-play image restora- tion with deep denoiser prior. IEEE Transactions on Pat- tern Analysis and Machine Intelligence , 44(10):6360–6376,

  59. [67]

    Hadamard single-pixel imaging versus fourier single-pixel imaging

    Zibang Zhang, Xueying Wang, Guoan Zheng, and Jin- gang Zhong. Hadamard single-pixel imaging versus fourier single-pixel imaging. Optics Express, 25(16):19619–19639,

  60. [68]

    Amp-net: Denoising-based deep unfolding for com- pressive image sensing

    Zhonghao Zhang, Yipeng Liu, Jiani Liu, Fei Wen, and Ce Zhu. Amp-net: Denoising-based deep unfolding for com- pressive image sensing. IEEE Transactions on Image Pro- cessing, 30:1487–1500, 2020. 2, 3, 6, 7

    2020

  61. [5557]

    2, 3, 6, 7

    PMLR, 2019. 2, 3, 6, 7

    2019

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.