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REVIEW 5 major objections 6 minor 47 references

A Tunable Despeckling Neural Network Stabilized via Diffusion Equation

T0 review · 5 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Unrolling a shallow denoiser with an implicit heat-equation step yields a SAR despeckling network that is provably convergent, stable, and resistant to adversarial attacks via a single tunable time step.

desk verdict A simple, plausible SAR-despeckling architecture with a tunable heat-equation block, but the convergence proof is not valid as written and the empirical case needs tighter reporting. read the letter →

arxiv 2411.15921 v2 pith:6JFUSNFZ submitted 2024-11-24 cs.CV eess.IV

Yi Ran , Zhichang Guo , Jia Li , Yao Li , Martin Burger , Boying Wu This is my paper · ORCID
classification cs.CVeess.IV MSC 68T0794A0835K0565M06
keywords ConvolutionalneuralnetworkadversarialattacksyntheticapertureradarimagedespecklingdiffusionequationmultiplicativeGammanoiseheatunrolledtunablesmoothness
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 tries to establish that unrolling a shallow denoising network together with an implicit heat-equation step yields a SAR despeckling network that is provably stable, tunable, and resistant to adversarial attacks. The key claim is that the diffusive block, because it dissipates high frequencies spontaneously, removes the high-frequency oscillations that adversarial perturbations induce in neural denoisers, without requiring adversarial training. The authors prove convergence and stability of the recursion under a non-expansiveness assumption on the denoiser, and support the claim with experiments on simulated gamma noise, adversarial samples, and real SAR images. If true, this gives a practical way to make learned despecklers robust to distribution shift by adjusting a single time-step hyperparameter after training.

What carries the argument

The central mechanism is the diffusion regularity block: the implicit heat-equation step $u_{k+1}=z_{k+1}+\tau\Delta u_{k+1}$, solved in the Fourier domain by multiplying by $1/(1-2\tau(\cos z_i+\cos z_j-2))$, so it acts as a fixed low-pass filter with a single tunable time step $\tau$. Unrolled $K$ times with a five-layer DnCNN block, the recursion accumulates regularization and yields the contraction proof: the resolvent norm $\|(I-\tau\Delta)^{-1}\|<1$ combined with the non-expansive denoiser gives a global contraction. This combines the fitting power of the neural block with the dissipative, noise-distribution-agnostic smoothing of the heat equation.

What would settle it

Compute the Lipschitz constant (maximum singular value of the Jacobian) of the trained $D_\Theta$ on the test set, or measure the contraction ratio $\|u_{k+1}-v_{k+1}\|/\|u_k-v_k\|$ for two nearby inputs through the full unrolled network; if the ratio exceeds 1 for any pair, the claimed global contraction—and the stability guarantee derived from it—fails as stated. Alternatively, run a white-box PGD attack directly against the proposed model and check whether high-frequency oscillations reappear.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that a linear heat equation, discretized implicitly and interleaved with a shallow DnCNN denoiser in a fixed-point recursion, acts as a regularity block that stabilizes the whole network. The update reads $z_{k+1}=D_\Theta(u_k)$, $u_{k+1}=z_{k+1}+\tau\Delta u_{k+1}$, so the diffusion step is the resolvent $(I-\tau\Delta)^{-1}$ applied to the denoiser output; the paper proves the sequence converges and the scheme is stable provided $D_\Theta$ is non-expansive. The same recursion lets a single parameter $\tau$ control output smoothness after training, and the authors show that increasing $\tau$ removes attack-induced oscillations while decreasing it preserves detail. Empirically, the model attains the best PSNR/SSIM on simulated data among the compared methods and visually removes oscillations on adversarial samples and real SAR images.

Load-bearing premise

The convergence and stability proof assumes the trained denoising network is non-expansive, yet the paper does not check that its five-layer DnCNN satisfies this, and the periodic-boundary implementation used in practice has a constant mode that makes the resolvent's contraction factor equal to 1 rather than strictly less.

Editorial extensions

If this is right

  • If the claim holds, learned SAR despecklers can gain adversarial robustness by inserting a classical diffusion prior rather than by adversarial training, cutting training cost and avoiding the need for attack samples.
  • The single time-step hyperparameter becomes a post-training control knob: operators can trade noise removal against detail preservation on real images without retraining.
  • The same unrolling pattern may transfer to other image restoration tasks where high-frequency artifacts are induced by distribution shift or attack.
  • The theoretical convergence guarantee, when the non-expansiveness premise is met, provides a certificate that the recursion's output does not depend sensitively on initialization or attack direction.
  • The model's performance gain over end-to-end CNNs suggests that hybrid model-driven/data-driven unrolling is a viable route to robust remote-sensing processing.

Reading between the lines

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

  • The paper's contraction argument relies on a strict contraction factor for the resolvent, which holds for Dirichlet but not periodic boundary conditions; a natural extension would be to verify whether the trained network's Jacobian norm stays below $1/\varepsilon$ on the data manifold, which would close the gap between the theorem and the implemented FFT solver.
  • Because the diffusion block is linear and fixed, its low-pass action is equivalent to a fixed convolutional layer; one could test whether learning that kernel (or making it anisotropic) preserves the robustness gain while improving detail retention.
  • The adversarial-robustness benefit may extend beyond denoising: the same dissipative block inserted after any feature extractor could damp oscillation-type adversarial perturbations in classification or detection, though the paper only demonstrates despeckling.
  • The experiments measure robustness via denoising-PGD transfer attacks from a specific 10-layer SAR-CNN; stronger attacks tailored to the proposed network itself might reveal the limits of the diffusive defense.
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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 / 6 minor

Summary. The paper proposes a SAR despeckling network obtained by unrolling a shallow five-layer DnCNN block and an implicit heat-equation block. The heat-equation block is solved by FFT under periodic boundary conditions, and a single time-step parameter τ can be changed after training to control output smoothness. The authors claim that the stability and convergence of the model are theoretically proven, that the diffusion block suppresses high-frequency oscillations caused by adversarial attacks, and that the method outperforms several state-of-the-art despeckling methods on simulated images, adversarial samples, and real SAR images.

Significance. If the theoretical guarantee were valid and the robustness benefit were rigorously demonstrated, the proposal would be a useful and interpretable unrolled architecture: it avoids adversarial training, needs only one tunable post-training parameter, and uses a simple FFT-based implicit diffusion block. The empirical core on simulated and real SAR images is plausible and includes comparisons with several relevant baselines. However, the paper's central theoretical claim is not established as written, and the adversarial-robustness evidence is weaker than the abstract suggests. The main value of the paper at present is the empirical framework and the tunable τ mechanism, not the claimed convergence theorem.

major comments (5)
  1. [III-D, Theorem 2] The theorem assumes that the denoising block DΘ is nonexpansive, but the block described in Section III-C is a five-layer DnCNN with ReLU activations, batch normalization, and residual connections, and no Lipschitz constraint is enforced or verified on the trained network. Without evidence that ∥DΘ(u1)−DΘ(u2)∥ ≤ ∥u1−u2∥ for the actually trained block, the contraction argument does not apply to the implemented model. The authors should either enforce nonexpansiveness (for example by spectral normalization or contractive activations) or verify it empirically and state the theorem conditionally on that verification.
  2. [III-D and III-E] The proof of Theorem 2 uses the bound ∥(I−τΔ)^{-1}∥ ≤ ε < 1, justified by claiming that −Δ is positive definite. However, the numerical scheme in Section III-E imposes periodic boundary conditions, under which the discrete Laplacian has a zero mode. In Eq. (10), the zero frequency (ξ_i = ξ_j = 0) gives denominator 1, so the resolvent has eigenvalue 1 and norm 1, not a value strictly below 1. With the implemented periodic scheme, the composition DΘ followed by the resolvent is at best nonexpansive, not a strict contraction, so the claimed global convergence does not follow from the stated argument. The theorem and the numerical scheme must be made consistent, for example by using Dirichlet boundary conditions matched to the discrete scheme, or by proving convergence under nonexpansiveness plus an additional compactness or asymptotic regularity argument.
  3. [III-D, Eq. (8)] Equation (8) contains a typographical error: the right-hand side reads DΘ(u_k) − DΘ(u_k), which is identically zero; it should be DΘ(u_k) − DΘ(v_k). This is a local error, but it obscures the proof and should be corrected in revision.
  4. [IV-D, Table II] The adversarial experiments do not yet substantiate the claim that the model 'effectively eliminates high-frequency oscillations induced by adversarial attacks'. Table II reports only PSNR on Set12, with a margin of 0.04 dB over the second-best method, and no SSIM, no perturbation budget, no error bars, and no attack targeted at the proposed model (the adversarial samples are transferred from a 10-layer SAR-CNN). The authors should report robustness under attacks generated against their own model, across several perturbation strengths, and with statistical significance measures.
  5. [IV-D, text] The sentence 'From quantitative index, our model is better than ours, but not too much' appears to be a typo and is confusing; it presumably should say 'better than the other methods' or similar. This is a presentation issue, but it matters because the quantitative advantage in Table II is small and needs a precise, non-contradictory description.
minor comments (6)
  1. [Algorithm 1] The denominator in Algorithm 1 uses cos(2π/N1 x_i) + cos(2π/N1 y_j), whereas Eq. (10) and the definitions of z_i and z_j use cos(2π/N1 x_i) + cos(2π/N2 y_j); for non-square images these differ, so the algorithm should be corrected to match the formula.
  2. [III-E and Table III] The text uses 'RPD-ROA' while Table III and the surrounding discussion use 'EPD-ROA'; the notation should be made consistent.
  3. [IV-B] The evaluation of real SAR images uses ENL, C_x, and EPD-ROA, but the paper does not specify how the homogeneous regions used to compute these metrics are selected; this should be stated for reproducibility.
  4. [IV-A] The test-set description says 12 and 14 images were picked randomly from FloodNet and RESISC45, but the dataset names in Table I list 'FloodNet' and 'NWPU'; 'NWPU' should be defined as RESISC45 or the table label should be changed.
  5. [II-B, Figure 2] Figure 2 is referenced as showing the low-pass property of the heat equation, but the caption does not define the color or line conventions; adding a short caption description would improve readability.
  6. [IV-C] The claim that the model provides 'superior detail preservation' is supported mainly by average PSNR/SSIM values; reporting standard deviations across the 10 noise realizations per image would strengthen the comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the framework and benchmarks are self-contained; the theoretical proof gap in Theorem 2 is a correctness issue, not a circular derivation.

full rationale

I walked the claimed derivation chain: the proposed model unrolls a shallow DnCNN block and an implicit heat-equation block with a tunable time step tau, trained end-to-end against simulated Gamma-noise data and evaluated on external benchmarks. No fitted parameter is renamed as a prediction: tau is a post-training dial, and the comparison methods are independent baselines. The self-citation to prior work [36] is motivational rather than load-bearing for the stability claim. The main theoretical statement, Theorem 2, assumes that DTheta is nonexpansive and asserts that ||(I - tau Delta)^{-1}|| < 1 because -Delta is positive definite; Section III-E then implements periodic boundary conditions, whose zero-frequency mode makes the resolvent eigenvalue exactly 1, and the trained five-layer DnCNN is not verified to be nonexpansive. This is a genuine gap in the proof as written, and it undercuts the abstract's unconditional claim that 'the stability and convergence of our model are theoretically proven.' However, this is not circularity: the nonexpansiveness hypothesis is an unverified stability-type assumption, not the theorem's conclusion, and the resolvent-norm issue is a mathematical error rather than the target result being presupposed by construction. The empirical robustness results remain independently testable. Thus, no self-definitional reduction, fitted-input prediction, or load-bearing self-citation chain is present; the appropriate finding is no significant circularity.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The method relies on standard PDE facts and a domain-specific noise model. The main fragility is in the convergence theorem, which assumes a nonexpansive denoiser and uses a resolvent norm bound that conflicts with the periodic boundary conditions used in the code-level scheme. Two hand-chosen hyperparameters, tau and K, control the regularizer.

free parameters (2)
  • tau (diffusion time step) = 0.1 during training; 0.02 to 0.18 at inference in experiments
    Hand-chosen hyperparameter controlling the strength of the heat equation regularizer; the tunable smoothness claim is exercised by changing this value after training.
  • K (unrolling depth) = 5
    Number of alternations between the denoiser block and the diffusion block; chosen by hand to balance computational cost and robustness.
assumptions (6)
  • domain assumption SAR observation model f = u*eta with Gamma noise of mean 1 and L looks (Eq. 1)
    The entire method and loss are built on this noise model; real SAR data may deviate, which motivates the robustness experiments.
  • standard math Heat equation solution is a convolution with the fundamental solution and is infinitely smooth; low-pass property attenuates high frequencies (Theorem 1, Eq. 2)
    Provides the theoretical basis for the regularization block.
  • ad hoc to paper The denoiser block DTheta is non-expansive (Theorem 2 assumption)
    Used to prove global convergence and stability, but no evidence is given that the 5-layer DnCNN with batch normalization satisfies it.
  • ad hoc to paper ||(I-tau Delta)^{-1}|| <= epsilon < 1 for the discrete operator (Theorem 2 proof)
    Stated as following from positive definiteness of -Delta, but the numerical scheme in Section III-E uses periodic boundary conditions, where the zero mode gives norm exactly 1; with Dirichlet boundary the norm is <1 but depends on the domain.
  • domain assumption Adversarial samples generated by denoising-PGD are a valid proxy for real-world distribution shift (Section II-A and IV-D)
    The paper uses transferability of denoising-PGD attacks to claim robustness on real SAR data.
  • domain assumption Logarithmic transformation converts multiplicative Gamma noise into additive noise with known nonzero mean c (Section III-C)
    Used to design the DnCNN block and loss; standard in SAR-CNN.

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Cite this review

Pith. "Pith review of A Tunable Despeckling Neural Network Stabilized via Diffusion Equation." pith.science (2026). https://pith.science/paper/6JFUSNFZ

@misc{pith2026241115921,
  author       = {Pith},
  title        = {Pith review of: A Tunable Despeckling Neural Network Stabilized via Diffusion Equation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6JFUSNFZ}},
  note         = {Machine review of arXiv:2411.15921}
}
read the original abstract

The removal of multiplicative Gamma noise is a critical research area in the application of synthetic aperture radar (SAR) imaging, where neural networks serve as a potent tool. However, real-world data often diverges from theoretical models, exhibiting various disturbances, which makes the neural network less effective. Adversarial attacks can be used as a criterion for judging the adaptability of neural networks to real data, since adversarial attacks can find the most extreme perturbations that make neural networks ineffective. In this work, the diffusion equation is designed as a regularization block to provide sufficient regularity to the whole neural network, due to its spontaneous dissipative nature. We propose a tunable, regularized neural network framework that unrolls a shallow denoising neural network block and a diffusion regularity block into a single network for end-to-end training. The linear heat equation, known for its inherent smoothness and low-pass filtering properties, is adopted as the diffusion regularization block. In our model, a single time step hyperparameter governs the smoothness of the outputs and can be adjusted dynamically, significantly enhancing flexibility. The stability and convergence of our model are theoretically proven. Experimental results demonstrate that the proposed model effectively eliminates high-frequency oscillations induced by adversarial attacks. Finally, the proposed model is benchmarked against several state-of-the-art denoising methods on simulated images, adversarial samples, and real SAR images, achieving superior performance in both quantitative and visual evaluations.

Figures

Figures reproduced from arXiv: 2411.15921 by the authors.

Figure 1
Figure 1. High frequency oscillations generated by adversarial attack. The 70th [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The results of the heat equation for different frequency signals as the time increases. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. framework of our model. perturbations is the core of adversarial attacks. In addition, the networks with stronger denoising effects on simulated data tend to be less robustness, which can be observed from [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: For details, given a set of training samples fi , yi(i = 1, · · · , N), where fi and yi represent noisy and clean images, respectively, the five layers DnCNN denoising module is used as the denoising block DΘ(·). It consists of five fully convolutional layers without a…
Figure 5
Figure 5. Figure 5: The structure of denoising block. condition that u = 0 on ∂Ω. Assume the neural network DΘ (·) is non-expandable: ∥DΘ (u1) − DΘ (u2) ∥ ⩽ ∥u1 − u2∥ Then, the sequence {u k} K k=0 generated by our algorithm is globally convergent. Proof. The proposed recursive algorithm …
Figure 7
Figure 7. Figure 7: Real SAR images. added to each image 10 times. Three real SAR images were used for evaluation of our method, as shown in [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 6
Figure 6. Figure 6: The results of our model with variance of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: Restoration results for images with enlarged areas of the same grayscale with noise level [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Restoration results for adversarial images based on noisy images with [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Restoration results for images with texture with noise level [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

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Reference graph

Works this paper leans on

47 extracted references · 30 canonical work pages

  1. [1]

    Interferometric synthetic aperture radar (sar) missions employing formation flying,

    G. Krieger, I. Hajnsek, K. P. Papathanassiou, M. Younis, and A. Mor- eira, “Interferometric synthetic aperture radar (sar) missions employing formation flying,” Proceedings of the IEEE, vol. 98, no. 5, pp. 816–843, 2010

    work page 2010

  2. [2]

    Learning a dilated residual network for sar image despeckling,

    Q. Zhang, Q. Yuan, J. Li, Z. Yang, and X. Ma, “Learning a dilated residual network for sar image despeckling,” Remote Sensing , vol. 10, no. 2, p. 196, 2018

    work page 2018

  3. [3]

    Polarimetric-spatial classification of sar images based on the fusion of multiple classifiers,

    X. Ma, H. Shen, J. Yang, L. Zhang, and P. Li, “Polarimetric-spatial classification of sar images based on the fusion of multiple classifiers,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 7, no. 3, pp. 961–971, 2013

    work page 2013

  4. [4]

    Some fundamental properties of speckle,

    J. W. Goodman, “Some fundamental properties of speckle,” JOSA, vol. 66, no. 11, pp. 1145–1150, 1976

    1976

  5. [5]

    Digital image enhancement and noise filtering by use of local statistics,

    J.-S. Lee, “Digital image enhancement and noise filtering by use of local statistics,” IEEE transactions on pattern analysis and machine intelligence, no. 2, pp. 165–168, 1980

    work page 1980

  6. [6]

    Adaptive noise smoothing filter for images with signal-dependent noise,

    D. T. Kuan, A. A. Sawchuk, T. C. Strand, and P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE transactions on pattern analysis and machine intelligence , no. 2, pp. 165–177, 1985

    work page 1985

  7. [7]

    A model for radar images and its application to adaptive digital filtering of multiplicative noise,

    V . S. Frost, J. A. Stiles, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Transactions on pattern analysis and machine intelligence, no. 2, pp. 157–166, 1982. 12

    work page 1982

  8. [8]

    Maximum a posteriori speckle filtering and first order texture models in sar images,

    A. Lopes, E. Nezry, R. Touzi, and H. Laur, “Maximum a posteriori speckle filtering and first order texture models in sar images,” in 10th annual international symposium on geoscience and remote sensing . Ieee, 1990, pp. 2409–2412

    work page 1990

Show all 47 references
  1. [9]

    A variational approach to removing multi- plicative noise,

    G. Aubert and J.-F. Aujol, “A variational approach to removing multi- plicative noise,” SIAM journal on applied mathematics , vol. 68, no. 4, pp. 925–946, 2008

    2008

  2. [10]

    A nonlinear inverse scale space method for a convex multiplicative noise model,

    J. Shi and S. Osher, “A nonlinear inverse scale space method for a convex multiplicative noise model,” SIAM Journal on imaging sciences , vol. 1, no. 3, pp. 294–321, 2008

    2008

  3. [11]

    A convex adaptive total variation model based on the gray level indicator for multiplicative noise removal,

    G. Dong, Z. Guo, B. Wu et al., “A convex adaptive total variation model based on the gray level indicator for multiplicative noise removal,” in Abstract and Applied Analysis , vol. 2013. Hindawi, 2013

    2013

  4. [12]

    A dou- bly degenerate diffusion model based on the gray level indicator for multiplicative noise removal,

    Z. Zhou, Z. Guo, G. Dong, J. Sun, D. Zhang, and B. Wu, “A dou- bly degenerate diffusion model based on the gray level indicator for multiplicative noise removal,” IEEE Transactions on Image Processing , vol. 24, no. 1, pp. 249–260, 2014

    2014

  5. [13]

    Image denoising based on a variable spatially exponent pde,

    A. Laghrib and L. Afraites, “Image denoising based on a variable spatially exponent pde,” Applied and Computational Harmonic Analysis, vol. 68, p. 101608, 2024

    2024

  6. [14]

    Multiplicative noise removal for texture images based on adaptive anisotropic fractional diffusion equations,

    W. Yao, Z. Guo, J. Sun, B. Wu, and H. Gao, “Multiplicative noise removal for texture images based on adaptive anisotropic fractional diffusion equations,” SIAM Journal on Imaging Sciences , vol. 12, no. 2, pp. 839–873, 2019

    2019

  7. [15]

    Multiplicative noise removal based on the smooth diffusion equation,

    X. Shan, J. Sun, and Z. Guo, “Multiplicative noise removal based on the smooth diffusion equation,” Journal of Mathematical Imaging and Vision, vol. 61, pp. 763–779, 2019

    2019

  8. [16]

    Sar image despeckling through convolutional neural networks,

    G. Chierchia, D. Cozzolino, G. Poggi, and L. Verdoliva, “Sar image despeckling through convolutional neural networks,” in 2017 IEEE international geoscience and remote sensing symposium (IGARSS) . IEEE, 2017, pp. 5438–5441

    2017

  9. [17]

    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

  10. [18]

    Sar image despeckling using a convolutional neural network,

    P. Wang, H. Zhang, and V . M. Patel, “Sar image despeckling using a convolutional neural network,” IEEE Signal Processing Letters , vol. 24, no. 12, pp. 1763–1767, 2017

    2017

  11. [19]

    Sar image despeckling using plug-and-play admm,

    S. Baraha and A. K. Sahoo, “Sar image despeckling using plug-and-play admm,” IET Radar, Sonar & Navigation, vol. 14, no. 9, pp. 1297–1309, 2020

    2020

  12. [20]

    Robustness to spatially-correlated speckle in plug-and-play polsar despeckling,

    C. U. Mendes, L. Denis, C. Deledalle, and F. Tupin, “Robustness to spatially-correlated speckle in plug-and-play polsar despeckling,” IEEE Transactions on Geoscience and Remote Sensing , 2024

    2024

  13. [21]

    Plug-and-play priors enabled sar image inpainting in the presence of speckle noise,

    S. Baraha and A. K. Sahoo, “Plug-and-play priors enabled sar image inpainting in the presence of speckle noise,” in 2020 IEEE 17th India Council International Conference (INDICON) . IEEE, 2020, pp. 1–6

    2020

  14. [22]

    Coupling model-and data-driven methods for remote sensing image restoration and fusion: Improving physical interpretability,

    H. Shen, M. Jiang, J. Li, C. Zhou, Q. Yuan, and L. Zhang, “Coupling model-and data-driven methods for remote sensing image restoration and fusion: Improving physical interpretability,” IEEE Geoscience and Remote Sensing Magazine , vol. 10, no. 2, pp. 231–249, 2022

    2022

  15. [23]

    Sar image despeckling employing a recursive deep cnn prior,

    H. Shen, C. Zhou, J. Li, and Q. Yuan, “Sar image despeckling employing a recursive deep cnn prior,” IEEE Transactions on Geoscience and Remote Sensing, vol. 59, no. 1, pp. 273–286, 2020

    2020

  16. [24]

    Deep un- rolling network for sar image despeckling,

    C. Chen, L. Chen, X. Jiang, X. Liu, and A. M. Zoubir, “Deep un- rolling network for sar image despeckling,” in ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2024, pp. 4085–4089

    2024

  17. [25]

    A comprehen- sive study on the robustness of deep learning-based image classification and object detection in remote sensing: Surveying and benchmarking,

    S. Mei, J. Lian, X. Wang, Y . Su, M. Ma, and L.-P. Chau, “A comprehen- sive study on the robustness of deep learning-based image classification and object detection in remote sensing: Surveying and benchmarking,” Journal of Remote Sensing , vol. 4, p. 0219, 2024

    2024

  18. [26]

    Explaining and harnessing adversarial examples,

    I. J. Goodfellow, J. Shlens, and C. Szegedy, “Explaining and harnessing adversarial examples,” arXiv preprint arXiv:1412.6572 , 2014

    2014 arXiv

  19. [27]

    Adversarial examples in the physical world,

    A. Kurakin, I. J. Goodfellow, and S. Bengio, “Adversarial examples in the physical world,” in Artificial intelligence safety and security . Chapman and Hall/CRC, 2018, pp. 99–112

    2018

  20. [28]

    Evaluating similitude and robustness of deep image denoising models via adversarial attack,

    J. Ning, J. Sun, Y . Li, Z. Guo, and W. Zuo, “Evaluating similitude and robustness of deep image denoising models via adversarial attack,” arXiv preprint arXiv:2306.16050, 2023

    2023 arXiv

  21. [29]

    Towards adver- sarially robust deep image denoising,

    H. Yan, J. Zhang, J. Feng, M. Sugiyama, and V . Y . Tan, “Towards adver- sarially robust deep image denoising,” arXiv preprint arXiv:2201.04397, 2022

    2022 arXiv

  22. [30]

    Agsdnet: Attention and gradient-based sar denoising network,

    R. K. Thakur and S. K. Maji, “Agsdnet: Attention and gradient-based sar denoising network,” IEEE Geoscience and Remote Sensing Letters , vol. 19, pp. 1–5, 2022

    2022

  23. [31]

    Towards deep learning models resistant to adversarial attacks,

    A. Madry, A. Makelov, L. Schmidt, D. Tsipras, and A. Vladu, “Towards deep learning models resistant to adversarial attacks,” stat, vol. 1050, no. 9, 2017

    2017

  24. [32]

    Adversarial training for free!

    A. Shafahi, M. Najibi, M. A. Ghiasi, Z. Xu, J. Dickerson, C. Studer, L. S. Davis, G. Taylor, and T. Goldstein, “Adversarial training for free!” Advances in neural information processing systems , vol. 32, 2019

    2019

  25. [33]

    Lipschitz regularized deep neural networks converge and generalize,

    A. M. Oberman and J. Calder, “Lipschitz regularized deep neural networks converge and generalize,” arXiv preprint arXiv:1808.09540 , 2018

    2018 arXiv

  26. [34]

    Clip: Cheap lipschitz training of neural networks,

    L. Bungert, R. Raab, T. Roith, L. Schwinn, and D. Tenbrinck, “Clip: Cheap lipschitz training of neural networks,” inInternational Conference on Scale Space and Variational Methods in Computer Vision. Springer, 2021, pp. 307–319

    2021

  27. [35]

    Lipschitz regularity of deep neural networks: analysis and efficient estimation,

    A. Virmaux and K. Scaman, “Lipschitz regularity of deep neural networks: analysis and efficient estimation,” Advances in Neural Infor- mation Processing Systems , vol. 31, 2018

    2018

  28. [36]

    A diffusion equation for improving the robustness of deep learning speckle removal model,

    L. Cheng, Y . Xing, Y . Li, and Z. Guo, “A diffusion equation for improving the robustness of deep learning speckle removal model,” Journal of Mathematical Imaging and Vision , pp. 1–21, 2024

    2024

  29. [37]

    Intriguing properties of neural networks,

    C. Szegedy, “Intriguing properties of neural networks,” arXiv preprint arXiv:1312.6199, 2013

    2013 arXiv

  30. [38]

    L. C. Evans, Partial differential equations . American Mathematical Society, 2022, vol. 19

    2022

  31. [39]

    Weickert et al., Anisotropic diffusion in image processing

    J. Weickert et al., Anisotropic diffusion in image processing . Teubner Stuttgart, 1998, vol. 1

    1998

  32. [40]

    A fast algorithm for euler’s elastica model using augmented lagrangian method,

    X.-C. Tai, J. Hahn, and G. J. Chung, “A fast algorithm for euler’s elastica model using augmented lagrangian method,” SIAM Journal on Imaging Sciences, vol. 4, no. 1, pp. 313–344, 2011

    2011

  33. [41]

    On single image scale-up using sparse-representations,

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

    2010

  34. [42]

    Color demosaicking by local directional interpolation and nonlocal adaptive thresholding,

    L. Zhang, X. Wu, A. Buades, and X. Li, “Color demosaicking by local directional interpolation and nonlocal adaptive thresholding,” Journal of Electronic imaging, vol. 20, no. 2, pp. 023 016–023 016, 2011

    2011

  35. [43]

    Floodnet: A high resolution aerial imagery dataset for post flood scene understanding,

    M. Rahnemoonfar, T. Chowdhury, A. Sarkar, D. Varshney, M. Yari, and R. Murphy, “Floodnet: A high resolution aerial imagery dataset for post flood scene understanding,” arXiv preprint arXiv:2012.02951 , 2020

    2012 arXiv

  36. [44]

    Remote sensing image scene classifi- cation: Benchmark and state of the art,

    G. Cheng, J. Han, and X. Lu, “Remote sensing image scene classifi- cation: Benchmark and state of the art,” Proceedings of the IEEE , vol. 105, no. 10, pp. 1865–1883, 2017

    2017

  37. [45]

    Batch normalization: Accelerating deep network training by reducing internal covariate shift,

    S. Ioffe, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 , 2015

    2015 arXiv

  38. [46]

    Mulog, or how to apply gaussian denoisers to multi-channel sar speckle reduction?

    C.-A. Deledalle, L. Denis, S. Tabti, and F. Tupin, “Mulog, or how to apply gaussian denoisers to multi-channel sar speckle reduction?” IEEE Transactions on Image Processing, vol. 26, no. 9, pp. 4389–4403, 2017

    2017

  39. [47]

    Transformer-based sar image despeckling,

    M. V . Perera, W. G. C. Bandara, J. M. J. Valanarasu, and V . M. Patel, “Transformer-based sar image despeckling,” inIGARSS 2022-2022 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2022, pp. 751–754

    2022

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.