You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors

Angelica I Aviles-Rivero; Carola-Bibiane Sch\"onlieb; Yanqi Cheng

REVIEW 3 major objections 4 minor 37 references

You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read The paper claims KAN denoisers enable Plug-and-Play inverse problems from a single noisy instance, with provable Lipschitz continuity and fixed-point convergence.

desk verdict The paper's central convergence theorem is false as stated, so the current version cannot be accepted; the KAN-as-single-shot-prior idea is worth revisiting after a serious fix. read the letter →

arxiv 2412.06204 v2 pith:PA7X3X2T submitted 2024-12-09 cs.CV

Yanqi Cheng , Carola-Bibiane Schönlieb , Angelica I Aviles-Rivero This is my paper · ORCID

classification cs.CV

keywords InverseProblemsPlug-and-PlayMethodsDeepDenoiserPriorsKolmogorov-ArnoldNetworksSingle-InstancePriorSuper-ResolutionConvergenceAnalysisADMM

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 introduces KAN-PnP, a Plug-and-Play optimization scheme that uses a Kolmogorov-Arnold Network (KAN) as the denoiser, trained on only the single noisy observation that is being restored. The central claim is that this single-instance prior removes the need for large training datasets while still giving stable, converging reconstructions. To back this, the authors prove that a KAN built from B-spline layers is Lipschitz continuous, and they argue that when the data fidelity term is convex and the ADMM penalty parameter exceeds the denoiser's Lipschitz constant, the iterates converge to a fixed point. Their experiments on super-resolution and joint demosaicing/deconvolution report that KAN-PnP matches or outperforms single-shot baselines such as INR, Noise2Self-FFDNet, and Noise2Self-UNet, often in as few as five iterations.

What carries the argument

The central object is the KAN denoiser $H_\sigma$, a composition of layers in which each layer computes $x_{l+1,j} = \sum_i \phi_{l,j,i}(x_{l,i})$ for univariate B-spline functions $\phi_{l,j,i}$ with bounded derivatives. The key estimate is Theorem 1: each spline has Lipschitz constant bounded by $C G^{k-1}$ (with $G$ grid points and smoothness order $k$), so the full network is Lipschitz with constant equal to the product of layer-wise maxima of these sums. This Lipschitz bound is what Theorem 2 feeds on: viewing the PnP-ADMM updates as a fixed-point iteration of a composed operator, the paper argues that a convex data fidelity term plus a penalty parameter $\mu > L_H$ makes the composition an averaged contraction, so the iterates converge by the Banach fixed-point theorem. The architecture's smooth B-spline interpolation also supplies the inductive bias that is claimed to make single-shot training avoid overfitting to noise.

What would settle it

Measure the actual Lipschitz constant of the trained KAN denoiser used in the experiments (for instance, by computing the maximum singular value of the Jacobian over the test images) and compare it with the ADMM penalty parameter $\mu$; if $L_H \ge \mu$ in any reported configuration, Theorem 2's premise fails and the claimed fixed-point guarantee does not cover that run.

Watch

Extended reading notes

Core claim

The paper's central discovery is that Kolmogorov-Arnold Networks, whose layers sum univariate B-spline functions of their inputs, are naturally well-conditioned as Plug-and-Play denoisers in the single-shot regime. Because each spline has bounded derivatives, the whole network has a Lipschitz constant bounded by the product of per-layer sums of spline bounds, so the denoiser is stable under input perturbations. The authors then show that PnP-ADMM with this denoiser converges to a fixed point $(x^*, z^*, u^*)$ satisfying $x^* = H_\sigma(z^* - u^*)$, $z^* = \operatorname{Prox}_{f/\mu}(x^* + u^*)$, and $x^* = z^*$, provided $f$ is proper, closed, and convex and the penalty parameter satisfies $\mu > L_H$. Empirically, the method achieves the best or tied PSNR/SSIM on super-resolution (2x, 4x, 8x) and on the joint demosaicing-plus-deconvolution task across datasets including Raccoon, Fractals, Wolf, and Butterfly, while converging in five ADMM iterations.

Load-bearing premise

The convergence proof assumes the trained network is smooth enough that its sensitivity to input changes stays below the algorithm's penalty strength, but the paper never measures or enforces that smoothness for the networks it actually runs.

Editorial extensions

If this is right

A denoiser trained on the single image being restored can replace dataset-trained denoisers in PnP, so inverse problems in data-scarce domains such as medical or scientific imaging become tractable without large training collections.
Because the method converges in about five ADMM iterations, per-image computational cost is low, making interactive or on-device restoration feasible.
The explicit Lipschitz bound gives a design rule for KAN denoisers: by choosing grid points, spline smoothness, and widths, practitioners can target $L_H \le 1$ (non-expansiveness) for even stronger convergence guarantees.
The same single-instance prior handles both pure super-resolution and joint tasks like demosaicing plus deconvolution, indicating the mechanism is not tied to one forward operator.
Theorem 2's fixed-point characterization provides a checkpoint condition $x^* = z^*$ that can be monitored in practice to detect convergence without knowing the implicit regularizer.

Reading between the lines

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

A practical follow-up would certify the convergence condition by measuring or upper-bounding the trained KAN denoiser's Lipschitz constant and checking it against the ADMM penalty before deployment.
The paper's five-iteration convergence is reported with a scheduled noise-level and penalty descent; varying that schedule while fixing the denoiser family would isolate how much of the speed comes from the KAN prior itself.
Because the single-instance prior trains on the noisy observation itself, it necessarily absorbs some noise statistics; testing KAN-PnP under structured or non-Gaussian noise would clarify whether the B-spline smoothness bias is what prevents overfitting to noise.
The same Lipschitz-based framework should transfer to other forward operators (e.g., nonlinear phase retrieval), since only the proximal data-fidelity step changes, providing a ready test of generality.

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.

Desk Editor's Note

read the letter

You should know two things about arXiv:2412.06204. First, the central convergence claim, Theorem 2, is not just unproven; it is false. Second, despite that, the paper has a legitimate kernel of an idea — using a KAN as a single-instance denoiser inside PnP — and the experiments, while thin, are honest enough to warrant a careful look if the theory is fixed.

What is new: the combination of KANs with PnP for single-shot inverse problems. That is a reasonable extension of the authors' earlier INR-based work [27], and the paper gives a straightforward Lipschitz bound for the B-spline KAN architecture. The empirical study covers super-resolution and joint demosaicing/deconvolution, and the ablation over KAN basis functions is a nice touch.

The soft spot is load-bearing. Theorem 2 claims convergence of PnP-ADMM whenever H is Lipschitz with constant L_H and the penalty parameter μ > L_H. The proof sketch asserts that composing a Lipschitz operator with a firmly nonexpansive proximal operator gives an averaged contraction. That is false. A concrete counterexample: H(x)=2x (L_H=2), f≡0, μ=3. All assumptions hold, yet the iterates double each step and diverge for any nonzero initial point. Lipschitz continuity alone with L_H≥1 does not imply nonexpansiveness, and μ>L_H does not make H contractive. The paper itself concedes in Section 2.2 that the implicit regulariser R need not exist, so the boundedness condition cannot repair the proof. The assumptions are also not verified for the trained network — they never compute L_H or enforce boundedness.

The experiments are a mixed bag. KAN-PnP usually beats or ties INR by a hair (e.g., 25.82 vs 25.80, 27.07 vs 27.06), and some entries are identical. There are no error bars, no code, and parameter counts differ by design. The comparison in Table 4 uses 5 iterations for KAN-PnP against 100–200 for BM3D/DIP-PnP, which is not apples-to-apples.

Who this is for: someone working on single-instance priors for inverse problems might find the empirical idea worth exploring, but the theoretical guarantee should be ignored until it is corrected. The paper needs major revision with a real fixed-point argument (or a more modest claim, e.g., convergence under a nonexpansive denoiser with L_H≤1, which the authors mention as future work).

My recommendation: send it to peer review, because the idea is novel enough to deserve expert scrutiny, but the current form would not survive — the theorem must be fixed or removed. I would not cite it as it stands.

Referee Report

3 major / 4 minor

Summary. The paper proposes KAN-PnP, a Plug-and-Play ADMM scheme in which a Kolmogorov-Arnold Network trained on a single noisy observation is used as the denoising prior. The authors state two theoretical results: Theorem 1 asserts that the KAN denoiser is Lipschitz continuous when built from B-splines with bounded coefficients and derivatives, and Theorem 2 asserts that PnP-ADMM with a Lipschitz denoiser and penalty parameter μ > L_H converges to a fixed point. The experimental section compares KAN-PnP with INR, FFDNet, UNet, BM3D, and TV priors on super-resolution and joint deconvolution/demosaicing, reporting small PSNR/SSIM improvements over the closest baseline.

Significance. If the claimed guarantees were valid, KAN-PnP would be a relevant contribution to single-instance PnP: it would provide a denoiser with an explicit Lipschitz bound and a fixed-point convergence guarantee under minimal data. The paper also provides an experimental comparison against several single-instance baselines, which is a useful step. However, the central theoretical claim is not sound: Theorem 2 is false as stated, and Theorem 1's conclusion depends on boundedness assumptions that are neither enforced nor verified. The manuscript therefore does not currently support its main advertised contribution.

major comments (3)

[Section 2.3, Theorem 2] The proof of Theorem 2 is invalid and the theorem is false as stated. Take f(x)=0 (proper, closed, and convex), H(x)=2x (2-Lipschitz), and μ=3>2. The updates in (17) reduce to x^{k+1}=2(z^k-u^k), z^{k+1}=x^{k+1}+u^k, and u^{k+1}=0, so x^{k+1}=z^{k+1}=2z^k. For any nonzero z^0 the iterates diverge while all hypotheses (i)-(iii) hold, contradicting the claimed convergence to a fixed point. The proof's key assertion that composing a Lipschitz operator with a firmly nonexpansive proximal operator yields an averaged contraction whenever μ>L_H is unsupported; Lipschitz continuity with L_H≥1 does not imply nonexpansiveness, and the condition μ>L_H does not make H contractive. The remark in Section 2.3 claiming convergence under this weaker assumption is therefore not justified by the cited fixed-point theory.
[Section 2.2 and Theorem 1] Theorem 1 concludes that the KAN denoiser is Lipschitz continuous only under assumptions of bounded spline coefficients and bounded derivatives, but the training procedure described in Section 3 does not enforce or verify these bounds, and no Lipschitz constant L_H is computed for the trained network. The paper itself concedes in Section 2.2 that the implicit regularizer R defined through (16) need not exist because Hσ may not be firmly nonexpansive. Consequently, the condition μ>L_H required by Theorem 2 is not checked for the algorithm actually run, and the boundedness of the regularisation functional invoked in the abstract is not one of the theorem's hypotheses.
[Section 3, training scheme] The experiments use a logarithmically decreasing penalty parameter and dynamically adjusted noise levels, whereas Theorem 2 assumes a constant penalty parameter μ and a fixed denoiser Hσ. The theorem therefore does not apply to the algorithm evaluated in Tables 1, 2, and 4. In particular, the empirical claim of convergence in five iterations has no theoretical backing from the only convergence result offered in the paper.

minor comments (4)

[Table 1] Several entries in Table 1 are implausibly low (for example, FFDNet-PnP on Giraffe at 2× is 4.29 dB and on Koala at 4× is 1.09 dB); these should be explained or corrected because they affect the reported comparison.
[Table 1] Many KAN-PnP results in Table 1 are identical or nearly identical to INR-PnP (e.g., 15.40, 16.21, 16.93, 23.05, 14.79, 17.46/17.47), which weakens the claim that KAN-PnP consistently outperforms INR; the text should acknowledge the closeness of these numbers.
[Reproducibility] The paper does not provide code, seeds, or a complete specification of the single-shot KAN training procedure, which makes the empirical results difficult to reproduce.
[Notation] Equation (5) uses λR(Hσ(z)) while the algorithm only uses Hσ; the paper states this is conceptual, but the notation should be flagged more clearly as an interpretation rather than a formal objective, because otherwise it conflicts with Section 2.2's admission that R need not exist.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the convergence theorem is conditional and its assumptions are unverified, but the claims do not reduce to their inputs or to self-citations.

full rationale

KAN-PnP's derivation chain is not circular. Theorem 1 establishes Lipschitz continuity of a KAN composed of bounded-coefficient B-splines; the bounded-coefficient condition is an input assumption, not a restatement of the theorem's conclusion. Theorem 2's fixed-point conditions (x*=H(z*-u*), z*=Prox_{f/µ}(x*+u*), x*=z*) are the natural stationarity equations of the ADMM iteration (17), not a disguised version of assumptions (i)-(iii). The paper explicitly disclaims relying on the implicit R in the convergence argument in Section 2.2: "we do not assume the explicit existence or convexity of R. Our convergence results rely on the Lipschitz continuity of Hσ, convexity of the data fidelity term, and boundedness of the surrogate regularisation." Thus Eq. (16) is presented as a conceptual proxy, not as a fitted parameter renamed as a prediction. The single-shot protocol trains the denoiser on the observed image itself, a deliberate methodological choice that may raise generalization concerns, but the reported PSNR values are not parameters fit to the ground-truth targets, and the same protocol is applied to all baselines. Self-citations [18] and [27] are background/comparison and are not used to justify Theorem 2; the proof instead cites external fixed-point works [10,12]. The skeptic's counterexample indicates Theorem 2 is unproven or false as stated, and the condition L_H<µ is not verified for the trained network; these are correctness and verification gaps, not circularity. No circular step can be exhibited, so the score is 0.

Assumptions & free parameters 6 free parameters · 4 assumptions · 1 invented entities

The central claims rest on several unverified assumptions: boundedness of the trained KAN parameters, existence of an implicit regularizer R, and a Lipschitz constant below the ADMM penalty parameter. These are introduced to make the convergence proof work but are not checked or enforced. The experimental hyperparameters are numerous and hand-selected, further increasing the ledger burden.

free parameters (6)

Pre-training noise standard deviation = 0.1
Chosen by hand in Section 3 training scheme; controls the denoiser training target.
Pre-training iterations = 100
Chosen by hand; stops training before full convergence, affecting the learned prior.
ADMM iterations = 5
Chosen by hand; the paper claims convergence in 5 iterations without ablation on this number.
Penalty parameter schedule = logarithmic descent
Described as 'dynamically adjusted' but not specified; affects ADMM convergence and results.
KAN architecture widths and grid = {128, 32, 16}, grid 5
Architecture choice; no ablation on widths or grid size.
Learning rate = 0.001
Standard choice; not tuned in the reported experiments.

assumptions (4)

standard math Kolmogorov-Arnold representation theorem justifies the use of KANs to approximate the denoising operator.
Invoked in Section 2.1 to motivate KANs, but the theorem does not guarantee the trained network approximates a denoiser with bounded spline derivatives.
domain assumption Spline coefficients of the trained KAN denoiser remain bounded so that the Lipschitz bound in Theorem 1 holds.
Section 2.2 states 'bounded spline parameters and regularisation' but no explicit constraint is imposed during single-shot training.
ad hoc to paper The implicit regularization functional R exists and is bounded below.
Used in the convergence discussion, but Section 2.2 admits R exists only if H is firmly nonexpansive, which is not guaranteed.
domain assumption The Lipschitz constant L_H of the trained denoiser is finite and satisfies L_H < µ.
Condition (iii) of Theorem 2; never verified for the trained network and not enforced by the algorithm.

invented entities (1)

Implicit regularization functional R
purpose: Conceptual regularizer in the variational formulation and in the boundedness assumption for convergence.
The paper explicitly treats R as conceptual and notes in Section 2.2 that it may not exist for a learned denoiser, so there is no falsifiable handle outside the paper.

how reviews work

0 comments

Cite this review

Pith. "Pith review of You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors." pith.science (2026). https://pith.science/paper/PA7X3X2T

@misc{pith2026241206204,
  author       = {Pith},
  title        = {Pith review of: You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PA7X3X2T}},
  note         = {Machine review of arXiv:2412.06204}
}

read the original abstract

The use of Plug-and-Play (PnP) methods has become a central approach for solving inverse problems, with denoisers serving as regularising priors that guide optimisation towards a clean solution. In this work, we introduce KAN-PnP, an optimisation framework that incorporates Kolmogorov-Arnold Networks (KANs) as denoisers within the Plug-and-Play (PnP) paradigm. KAN-PnP is specifically designed to solve inverse problems with single-instance priors, where only a single noisy observation is available, eliminating the need for large datasets typically required by traditional denoising methods. We show that KANs, based on the Kolmogorov-Arnold representation theorem, serve effectively as priors in such settings, providing a robust approach to denoising. We prove that the KAN denoiser is Lipschitz continuous, ensuring stability and convergence in optimisation algorithms like PnP-ADMM, even in the context of single-shot learning. Additionally, we provide theoretical guarantees for KAN-PnP, demonstrating its convergence under key conditions: the convexity of the data fidelity term, Lipschitz continuity of the denoiser, and boundedness of the regularisation functional. These conditions are crucial for stable and reliable optimisation. Our experimental results show, on super-resolution and joint optimisation, that KAN-PnP outperforms exiting methods, delivering superior performance in single-shot learning with minimal data. The method exhibits strong convergence properties, achieving high accuracy with fewer iterations.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

37 extracted references · 28 canonical work pages

[27]

Transactions on Machine Learning Research (2024)

Cheng, Y., Zhang, L., Shen, Z., Wang, S., Yu, L., Chan, R.H., Sch¨ onlieb, C.- B., Aviles-Rivero, A.I.: Single-shot plug-and-play methods for inverse problems. Transactions on Machine Learning Research (2024)

work page 2024
[1]

IEEE signal processing magazine 27(4), 81–89 (2010) 19

Fessler, J.A.: Model-based image reconstruction for mri. IEEE signal processing magazine 27(4), 81–89 (2010) 19

work page 2010
[2]

IEEE transactions on medical imaging 21(2), 89–99 (2002)

Elbakri, I.A., Fessler, J.A.: Statistical image reconstruction for polyenergetic x- ray computed tomography. IEEE transactions on medical imaging 21(2), 89–99 (2002)

work page 2002
[3]

Mir (1987)

Tikhonov, A.N., Goncharsky, A., Bloch, M.: Ill-posed problems in the natural sciences. Mir (1987)

work page 1987
[4]

Mathematics and its Applications 375 (1996)

Engl, H.: Regularization of inverse problems. Mathematics and its Applications 375 (1996)

work page 1996
[5]

Acta Numerica 25, 161–319 (2016)

Chambolle, A., Pock, T.: An introduction to continuous optimization for imaging. Acta Numerica 25, 161–319 (2016)

work page 2016
[6]

Journal of Mathematical Imaging and Vision 62(6), 773–789 (2020)

Gribonval, R., Nikolova, M.: A characterization of proximity operators. Journal of Mathematical Imaging and Vision 62(6), 773–789 (2020)

work page 2020
[7]

Computers & mathematics with applications 2(1), 17–40 (1976)

Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear varia- tional problems via finite element approximation. Computers & mathematics with applications 2(1), 17–40 (1976)

work page 1976

Show all 37 references

[8]

In: 2013 IEEE Global Conference on Signal and Information Processing, pp

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

2013
[9]

In: Proceedings of the IEEE International Conference on Computer Vision, pp

Meinhardt, T., Moller, M., Hazirbas, C., Cremers, D.: Learning proximal oper- ators: Using denoising networks for regularizing inverse imaging problems. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1781–1790 (2017)

2017
[10]

In: International Conference on Machine Learning, pp

Ryu, E., Liu, J., Wang, S., Chen, X., Wang, Z., Yin, W.: Plug-and-play methods provably converge with properly trained denoisers. In: International Conference on Machine Learning, pp. 5546–5557 (2019). PMLR

2019
[11]

IEEE Transactions on Computational Imaging 5(3), 395–408 (2019)

Sun, Y., Wohlberg, B., Kamilov, U.S.: An online plug-and-play algorithm for regularized image reconstruction. IEEE Transactions on Computational Imaging 5(3), 395–408 (2019)

2019
[12]

In: International Conference on Machine Learning, pp

Hurault, S., Leclaire, A., Papadakis, N.: Proximal denoiser for convergent plug-and-play optimization with nonconvex regularization. In: International Conference on Machine Learning, pp. 9483–9505 (2022). PMLR

2022
[13]

arXiv preprint arXiv:2110.03220 (2021)

Hurault, S., Leclaire, A., Papadakis, N.: Gradient step denoiser for convergent plug-and-play. arXiv preprint arXiv:2110.03220 (2021)

2021 arXiv
[14]

IEEE Transactions on Image Processing 28(1), 451–463 (2018) 20

Teodoro, A.M., Bioucas-Dias, J.M., Figueiredo, M.A.: A convergent image fusion algorithm using scene-adapted gaussian-mixture-based denoising. IEEE Transactions on Image Processing 28(1), 451–463 (2018) 20

2018
[15]

In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp

Yuan, X., Liu, Y., Suo, J., Dai, Q.: Plug-and-play algorithms for large-scale snapshot compressive imaging. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1447–1457 (2020)

2020
[16]

In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp

Zhang, K., Zuo, W., Gu, S., Zhang, L.: Learning deep cnn denoiser prior for image restoration. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3929–3938 (2017)

2017
[17]

IEEE Signal Processing Letters 24(8), 1108–1112 (2017)

Ono, S.: Primal-dual plug-and-play image restoration. IEEE Signal Processing Letters 24(8), 1108–1112 (2017)

2017
[18]

In: International Conference on Machine Learning, pp

Wei, K., Aviles-Rivero, A., Liang, J., Fu, Y., Sch¨ onlieb, C.-B., Huang, H.: Tuning-free plug-and-play proximal algorithm for inverse imaging problems. In: International Conference on Machine Learning, pp. 10158–10169 (2020). PMLR

2020
[19]

IEEE Transactions on image processing 16(8), 2080–2095 (2007)

Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Transactions on image processing 16(8), 2080–2095 (2007)

2007
[20]

Jordan, C.: Sur la series de fourier. CR Acad. Sci., Paris 92, 228–230 (1881)
[21]

SIAM Journal on Imaging Sciences 15(2), 701–737 (2022)

Laumont, R., Bortoli, V.D., Almansa, A., Delon, J., Durmus, A., Pereyra, M.: Bayesian imaging using plug & play priors: when langevin meets tweedie. SIAM Journal on Imaging Sciences 15(2), 701–737 (2022)

2022
[22]

IEEE transactions on image processing 26(7), 3142–3155 (2017)

Zhang, K., Zuo, W., Chen, Y., Meng, D., Zhang, L.: Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising. IEEE transactions on image processing 26(7), 3142–3155 (2017)

2017
[23]

In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, pp

Ronneberger, O., Fischer, P., Brox, T.: U-net: Convolutional networks for biomed- ical image segmentation. In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, p...

2015
[24]

SIAM Journal on Imaging Sciences 17(1), 91–115 (2024)

Goujon, A., Neumayer, S., Unser, M.: Learning weakly convex regularizers for convergent image-reconstruction algorithms. SIAM Journal on Imaging Sciences 17(1), 91–115 (2024)

2024
[25]

In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp

Ulyanov, D., Vedaldi, A., Lempitsky, V.: Deep image prior. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9446–9454 (2018)

2018
[26]

In: ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp

Sun, Z., Latorre, F., Sanchez, T., Cevher, V.: A plug-and-play deep image prior. In: ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 8103–8107 (2021). IEEE 21

2021
[28]

arXiv preprint arXiv:2404.19756 (2024)

Liu, Z., Wang, Y., Vaidya, S., Ruehle, F., Halverson, J., Soljaˇ ci´ c, M., Hou, T.Y., Tegmark, M.: Kan: Kolmogorov-arnold networks. arXiv preprint arXiv:2404.19756 (2024)

2024 arXiv
[29]

In: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol

Buades, A., Coll, B., Morel, J.-M.: A non-local algorithm for image denoising. In: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 2, pp. 60–65 (2005). Ieee

2005
[30]

American Mathematical Society (1961)

Kolmogorov, A.N.: On the representation of continuous functions of several vari- ables by superpositions of continuous functions of a smaller number of variables. American Mathematical Society (1961)

1961
[31]

In: Dokl

Kolmogorov, A.N.: On the representations of continuous functions of many vari- ables by superposition of continuous functions of one variable and addition. In: Dokl. Akad. Nauk USSR, vol. 114, pp. 953–956 (1957)

1957
[32]

Constructive approximation 30, 653–675 (2009)

Braun, J., Griebel, M.: On a constructive proof of kolmogorov’s superposition theorem. Constructive approximation 30, 653–675 (2009)

2009
[33]

Bevilacqua, M., Roumy, A., Guillemot, C., Alberi-Morel, M.L.: Low-complexity single-image super-resolution based on nonnegative neighbor embedding (2012)

2012
[34]

In: Curves and Surfaces: 7th International Conference, Avignon, France, June 24-30, 2010, Revised Selected Papers 7, pp

Zeyde, R., Elad, M., Protter, M.: On single image scale-up using sparse- representations. In: Curves and Surfaces: 7th International Conference, Avignon, France, June 24-30, 2010, Revised Selected Papers 7, pp. 711–730 (2012). Springer

2012
[35]

ACM Transactions on Graphics (TOG) 42(4), 1–19 (2023)

Lai, Z., Wei, K., Fu, Y., H¨ artel, P., Heide, F.: δ-prox: Differentiable proximal algorithm modeling for large-scale optimization. ACM Transactions on Graphics (TOG) 42(4), 1–19 (2023)

2023
[36]

In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp

Krull, A., Buchholz, T.-O., Jug, F.: Noise2void-learning denoising from single noisy images. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 2129–2137 (2019)

2019
[37]

IEEE Transactions on Image Processing 27(9), 4608–4622 (2018) 22

Zhang, K., Zuo, W., Zhang, L.: Ffdnet: Toward a fast and flexible solution for cnn- based image denoising. IEEE Transactions on Image Processing 27(9), 4608–4622 (2018) 22

2018

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [27]

Transactions on Machine Learning Research (2024)

Cheng, Y., Zhang, L., Shen, Z., Wang, S., Yu, L., Chan, R.H., Sch¨ onlieb, C.- B., Aviles-Rivero, A.I.: Single-shot plug-and-play methods for inverse problems. Transactions on Machine Learning Research (2024)

work page 2024

[2] [1]

IEEE signal processing magazine 27(4), 81–89 (2010) 19

Fessler, J.A.: Model-based image reconstruction for mri. IEEE signal processing magazine 27(4), 81–89 (2010) 19

work page 2010

[3] [2]

IEEE transactions on medical imaging 21(2), 89–99 (2002)

Elbakri, I.A., Fessler, J.A.: Statistical image reconstruction for polyenergetic x- ray computed tomography. IEEE transactions on medical imaging 21(2), 89–99 (2002)

work page 2002

[4] [3]

Mir (1987)

Tikhonov, A.N., Goncharsky, A., Bloch, M.: Ill-posed problems in the natural sciences. Mir (1987)

work page 1987

[5] [4]

Mathematics and its Applications 375 (1996)

Engl, H.: Regularization of inverse problems. Mathematics and its Applications 375 (1996)

work page 1996

[6] [5]

Acta Numerica 25, 161–319 (2016)

Chambolle, A., Pock, T.: An introduction to continuous optimization for imaging. Acta Numerica 25, 161–319 (2016)

work page 2016

[7] [6]

Journal of Mathematical Imaging and Vision 62(6), 773–789 (2020)

Gribonval, R., Nikolova, M.: A characterization of proximity operators. Journal of Mathematical Imaging and Vision 62(6), 773–789 (2020)

work page 2020

[8] [7]

Computers & mathematics with applications 2(1), 17–40 (1976)

Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear varia- tional problems via finite element approximation. Computers & mathematics with applications 2(1), 17–40 (1976)

work page 1976