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arxiv: 2605.13744 · v1 · submitted 2026-05-13 · 💻 cs.CV

Recognition: 2 theorem links

· Lean Theorem

Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration

Feiyu Tan , Qi Xie , Zongben Xu , Deyu Meng

Authors on Pith no claims yet

Pith reviewed 2026-05-14 19:48 UTC · model grok-4.3

classification 💻 cs.CV
keywords image restorationequivariancedata symmetryinverse problemadaptive networksuper-resolutiondenoisingderaining
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The pith

Equivariance error of the optimal restoration operator is strictly bounded by data symmetry error and discretization mesh size.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a direct theoretical link between the symmetry present in real-world image data and the equivariance properties that restoration networks should possess. It introduces a measurable definition of non-strict symmetry defined over entire datasets rather than individual samples, then uses this as a constraint when casting the restoration task as an inverse problem. From this formulation the authors derive that the equivariance error of the best possible restoration operator cannot exceed the sum of the data symmetry error and the discretization mesh size. They further show that matching network equivariance to this data symmetry level improves the bias-variance trade-off and thereby lowers overall expected risk. These results motivate a practical adaptive architecture that learns per-sample symmetry alignment.

Core claim

We propose a quantifiable definition of non-strict symmetry at the dataset level and incorporate it as a constraint when formulating the image restoration inverse problem. The equivariance of restoration models follows directly from this constrained formulation, and the equivariance error of the optimal operator is strictly bounded by the data symmetry error together with the discretization mesh size. Analysis of empirical risk demonstrates that aligning network equivariance to the measured data symmetry optimizes the bias-variance tradeoff and minimizes total expected risk.

What carries the argument

Quantifiable non-strict symmetry defined at the dataset level, used as an explicit constraint in the inverse-problem formulation from which model equivariance is derived and bounded.

If this is right

  • Equivariant networks chosen without reference to measured data symmetry will carry unnecessary equivariance error on imperfectly symmetric data.
  • The bias-variance decomposition of restoration risk is minimized precisely when network equivariance matches the dataset symmetry level.
  • A hypernetwork-driven adaptive equivariant convolution can dynamically adjust to each sample's symmetry and thereby realize the theoretical risk reduction.
  • The same symmetry-constrained formulation applies to super-resolution, denoising, and deraining, each of which shows improved performance once alignment is enforced.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The dataset-level symmetry measure could be used to decide which transformation group to embed in networks for other inverse problems such as inpainting or deblurring.
  • The bound relating equivariance error to symmetry error suggests a practical diagnostic: compute symmetry error on a new dataset first, then set the target equivariance tolerance accordingly.
  • If the mesh-size term dominates in high-resolution regimes, coarser discretizations may need explicit correction terms to keep total error controlled.

Load-bearing premise

The proposed definition of non-strict symmetry at the dataset level can serve as a valid constraint for formulating the restoration inverse problem on real data that only approximately obeys geometric symmetries.

What would settle it

Construct a controlled dataset whose symmetry error and mesh size are known exactly, train or optimize the corresponding restoration operator, and measure whether its equivariance error ever exceeds the sum of those two quantities.

Figures

Figures reproduced from arXiv: 2605.13744 by Deyu Meng, Feiyu Tan, Qi Xie, Zongben Xu.

Figure 1
Figure 1. Figure 1: Overview of the structure of this work. To address the limitations of existing [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Histograms of the symmetry met￾ric εG for three constraint scenarios under five different regularizers. (b) Take TV as an exam￾ple, the local feature responses under varying rotation angles across three scenarios [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of (a) adaptive transformation group family and filter parametrization; [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The process of feature extraction from images using classical differential kernels. [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visual comparison of ×2 SR results from various methods on img011 of Urban100 [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visual comparison of ×2 SR results from various methods on img2731 of RSSCN7. to capture richer symmetries and set the channel number as 1/8 to the original networks in each layer to keep memory consumption similar. Datasets and Training Settings. To validate the generalization and robustness of the proposed method across diverse visual domains, we conduct experiments on two distinct types of imagery. For … view at source ↗
Figure 7
Figure 7. Figure 7: Visual results of Denoising from various methods on img039 of Urban100. [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Visual results of Denoising from various methods on img046 of Ada4DIR. [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Visual results of Rain removal from various methods on img024 of Rain100L. [PITH_FULL_IMAGE:figures/full_fig_p027_9.png] view at source ↗
read the original abstract

Image restoration is an inherently ill posed inverse problem. Equivariant networks that embed geometric symmetry priors can mitigate this ill posedness and improve performance. However, current understanding of the relationship between network equivariance and data symmetry remains largely heuristic. Particularly for real world data with imperfect symmetry, existing research lacks a systematic theoretical framework to quantify symmetry, select transformation groups, or evaluate model data alignment. To bridge this gap, we conduct an analysis from an optimization perspective and formalize the intrinsic relationship among data symmetry priors, model equivariance, and generalization capability. Specifically, we propose for the first time a quantifiable definition of non strict symmetry at the dataset level (rather than sample level) and use it as a constraint to formulate the restoration inverse problem. We then show that the equivariance for restoration models can be naturally derived from this inverse problems incorporated the proposed symmetry constraints, and that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size. Furthermore, by analyzing the network's empirical risk, we demonstrate that aligning equivariance with data symmetry optimizes the bias variance trade off, minimizing the total expected risk. Guided by these insights, we propose a Sample Adaptive Equivariant Network that uses a hypernetwork and transformation learnable equivariant convolutions to dynamically align with each sample's inherent symmetry. Extensive experiments on super resolution, denoising, and deraining validate our theoretical findings and show significant superiority over standard baselines and traditional equivariant models. Our code and supplementary material are available at https://github.com/tanfy929/SA-Conv.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper claims to formalize the relationship between data symmetry, network equivariance, and generalization in image restoration from an optimization viewpoint. It introduces a quantifiable definition of non-strict symmetry at the dataset level (rather than per-sample), incorporates it as a constraint in the inverse problem, derives that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error plus discretization mesh size, and shows via empirical risk analysis that alignment optimizes the bias-variance tradeoff to minimize total expected risk. Guided by this, it proposes the Sample Adaptive Equivariant Network (SA-Conv) using a hypernetwork and learnable equivariant convolutions, with experiments on super-resolution, denoising, and deraining demonstrating superiority over baselines.

Significance. If the bounds and risk analysis are valid, the work supplies a systematic, optimization-based account of how to choose and adapt equivariance groups for restoration networks under imperfect real-world symmetries, moving beyond heuristic priors. The adaptive SA-Conv design offers a concrete mechanism for per-sample alignment that could improve generalization in ill-posed inverse problems.

major comments (3)
  1. [Abstract / §3] Abstract and the inverse-problem formulation (likely §3): the central bound on equivariance error treats the single dataset-level non-strict symmetry measure as a hard constraint that propagates uniformly to every sample. Real data symmetries (rotation, reflection) vary across samples, so a global statistic supplies only an average; no uniformity assumption or per-sample error propagation step is supplied to justify the strict bound for individual instances.
  2. [§4] Empirical-risk and bias-variance section (likely §4): the argument that alignment minimizes total expected risk rests on standard ERM but does not show how the dataset-wide symmetry constraint modifies the per-sample risk term when symmetry deviates from the mean. Without this link the claimed optimization of the tradeoff is not load-bearing.
  3. [§3.2] Theorem or proposition stating the strict bound (likely Eq. (X) in §3.2): the bound is asserted to follow directly from the optimization perspective, yet the provided abstract and skeptic analysis give no proof sketch or explicit dependence on the mesh size; verification requires the full derivation to confirm it is not circular with the symmetry definition itself.
minor comments (2)
  1. [§2] Notation for the dataset-level symmetry measure should be introduced with an explicit equation rather than descriptive text only.
  2. [§5] Experimental tables would benefit from error bars or multiple runs to support the reported superiority claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments that help clarify the presentation of our theoretical framework. We address each major comment point by point below, providing explanations grounded in the manuscript's derivations and indicating where revisions will be made for improved clarity.

read point-by-point responses

  1. Referee: [Abstract / §3] Abstract and the inverse-problem formulation (likely §3): the central bound on equivariance error treats the single dataset-level non-strict symmetry measure as a hard constraint that propagates uniformly to every sample. Real data symmetries (rotation, reflection) vary across samples, so a global statistic supplies only an average; no uniformity assumption or per-sample error propagation step is supplied to justify the strict bound for individual instances.

    Authors: We agree that symmetries vary across samples in real data. The dataset-level non-strict symmetry is defined as an aggregate measure over the data distribution and is incorporated as a global constraint in the inverse-problem formulation in Section 3. The strict bound on equivariance error applies to the optimal restoration operator obtained under this constraint; it is not asserted to hold uniformly for arbitrary per-sample deviations but rather characterizes the operator's behavior with respect to the dataset symmetry error. The per-sample variations are explicitly addressed by the adaptive mechanism in SA-Conv (Section 5). We will add a clarifying remark in Section 3 stating the uniformity assumption implicit in the global constraint and note that per-sample alignment is handled separately via adaptation. revision: partial

  2. Referee: [§4] Empirical-risk and bias-variance section (likely §4): the argument that alignment minimizes total expected risk rests on standard ERM but does not show how the dataset-wide symmetry constraint modifies the per-sample risk term when symmetry deviates from the mean. Without this link the claimed optimization of the tradeoff is not load-bearing.

    Authors: In Section 4, the empirical risk analysis begins from the standard ERM decomposition but incorporates the dataset-level symmetry constraint into the bias term of the bias-variance tradeoff. The constraint modifies the expected risk by bounding the deviation from equivariance, and the alignment (via SA-Conv) reduces the variance component when per-sample symmetry deviates from the dataset mean. We will expand this section with an explicit derivation showing how the global constraint propagates to the per-sample risk term under deviation from the mean, making the optimization argument self-contained. revision: yes

  3. Referee: [§3.2] Theorem or proposition stating the strict bound (likely Eq. (X) in §3.2): the bound is asserted to follow directly from the optimization perspective, yet the provided abstract and skeptic analysis give no proof sketch or explicit dependence on the mesh size; verification requires the full derivation to confirm it is not circular with the symmetry definition itself.

    Authors: The full derivation of the bound, including its explicit dependence on the discretization mesh size of the transformation group, appears in Section 3.2 together with the supporting lemmas in the appendix. The symmetry error is defined independently via the dataset-level measure on the data distribution and group actions; the bound then follows from the first-order optimality condition of the constrained inverse problem without circularity. We will insert a concise proof sketch of the key steps (including the mesh-size term) into the main text of Section 3.2 for easier verification. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation builds from new definition without reducing to tautology

full rationale

The paper introduces a novel quantifiable definition of non-strict dataset-level symmetry and inserts it as a constraint into the restoration inverse problem formulation. From this setup it derives that the optimal operator's equivariance error is bounded by the defined symmetry error plus mesh size, and that alignment optimizes bias-variance. These steps constitute a standard forward derivation from the proposed constraint rather than any reduction of the claimed bound or risk result back to a fitted quantity or self-citation by construction. The empirical-risk analysis rests on conventional arguments independent of the new symmetry measure. No load-bearing equation or claim collapses to its own inputs; the framework is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The framework rests on standard optimization theory for inverse problems and group-equivariance concepts from prior literature; the new symmetry definition is introduced without explicit free parameters or additional invented entities beyond the adaptive network itself.

axioms (2)
  • standard math Standard assumptions of optimization theory for ill-posed inverse problems
    Used to formulate the restoration problem as an optimization task incorporating symmetry constraints.
  • domain assumption Group theory foundations for equivariant convolutions
    Basis for defining and implementing equivariant network layers.
invented entities (1)
  • Sample Adaptive Equivariant Network (SA-Conv) no independent evidence
    purpose: Dynamically align equivariance with each sample's inherent symmetry via hypernetwork and learnable convolutions
    New architecture proposed to implement the theoretical alignment; no independent evidence outside the paper is provided.

pith-pipeline@v0.9.0 · 5596 in / 1521 out tokens · 82668 ms · 2026-05-14T19:48:24.213823+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

70 extracted references · 70 canonical work pages · 2 internal anchors

  1. [1]

    Communications of the ACM , volume=

    The JPEG still picture compression standard , author=. Communications of the ACM , volume=. 1991 , publisher=

    work page 1991

  2. [2]

    IEEE transactions on pattern analysis and machine intelligence , volume=

    Effects of image degradation and degradation removal to CNN-based image classification , author=. IEEE transactions on pattern analysis and machine intelligence , volume=. 2019 , publisher=

    work page 2019

  3. [3]

    IEEE Transactions on Acoustics, Speech, and Signal Processing , volume=

    Image reconstruction and restoration: Overview of common estimation structures and problems , author=. IEEE Transactions on Acoustics, Speech, and Signal Processing , volume=. 2002 , publisher=

    work page 2002

  4. [4]

    SIAM Journal on Scientific Computing , volume=

    Iterative algorithms based on decoupling of deblurring and denoising for image restoration , author=. SIAM Journal on Scientific Computing , volume=. 2008 , publisher=

    work page 2008

  5. [5]

    IEEE Geoscience and Remote Sensing Magazine , volume=

    Image restoration for remote sensing: Overview and toolbox , author=. IEEE Geoscience and Remote Sensing Magazine , volume=. 2021 , publisher=

    work page 2021

  6. [6]

    SIAM Journal on Imaging Sciences , volume=

    A reweighted joint spatial-radon domain CT image reconstruction model for metal artifact reduction , author=. SIAM Journal on Imaging Sciences , volume=. 2018 , publisher=

    work page 2018

  7. [7]

    Psychological Science , volume=

    Face recognition in poor-quality video: Evidence from security surveillance , author=. Psychological Science , volume=. 1999 , publisher=

    work page 1999

  8. [8]

    2011 , publisher=

    Digital imaging for cultural heritage preservation , author=. 2011 , publisher=

    work page 2011

  9. [9]

    International conference Inverse problems: modelling and simulation , pages=

    Inverse Problems in Image Restoration , author=. International conference Inverse problems: modelling and simulation , pages=. 2024 , organization=

    work page 2024

  10. [10]

    SIAM Journal on Imaging Sciences , volume=

    Preconditioned plug-and-play ADMM with locally adjustable denoiser for image restoration , author=. SIAM Journal on Imaging Sciences , volume=. 2023 , publisher=

    work page 2023

  11. [11]

    2002 , publisher=

    Computational methods for inverse problems , author=. 2002 , publisher=

    work page 2002

  12. [12]

    Physica D: nonlinear phenomena , volume=

    Nonlinear total variation based noise removal algorithms , author=. Physica D: nonlinear phenomena , volume=. 1992 , publisher=

    work page 1992

  13. [13]

    IEEE transactions on pattern analysis and machine intelligence , volume=

    Trainable nonlinear reaction diffusion: A flexible framework for fast and effective image restoration , author=. IEEE transactions on pattern analysis and machine intelligence , volume=. 2016 , publisher=

    work page 2016

  14. [14]

    IEEE transactions on image processing , volume=

    Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising , author=. IEEE transactions on image processing , volume=. 2017 , publisher=

    work page 2017

  15. [15]

    Journal of mathematical imaging and vision , volume=

    A first-order primal-dual algorithm for convex problems with applications to imaging , author=. Journal of mathematical imaging and vision , volume=. 2011 , publisher=

    work page 2011

  16. [16]

    IEEE Transactions on Computational Imaging , volume=

    Plug-and-play ADMM for image restoration: Fixed-point convergence and applications , author=. IEEE Transactions on Computational Imaging , volume=. 2016 , publisher=

    work page 2016

  17. [17]

    IEEE transactions on pattern analysis and machine intelligence , volume=

    Image super-resolution using deep convolutional networks , author=. IEEE transactions on pattern analysis and machine intelligence , volume=. 2015 , publisher=

    work page 2015

  18. [18]

    Proceedings of the IEEE conference on computer vision and pattern recognition workshops , pages=

    Enhanced deep residual networks for single image super-resolution , author=. Proceedings of the IEEE conference on computer vision and pattern recognition workshops , pages=

    work page

  19. [19]

    IEEE Transactions on Neural Networks and Learning Systems , volume=

    RCDNet: An interpretable rain convolutional dictionary network for single image deraining , author=. IEEE Transactions on Neural Networks and Learning Systems , volume=. 2023 , publisher=

    work page 2023

  20. [20]

    SIAM journal on imaging sciences , volume=

    A fast iterative shrinkage-thresholding algorithm for linear inverse problems , author=. SIAM journal on imaging sciences , volume=. 2009 , publisher=

    work page 2009

  21. [21]

    arXiv preprint arXiv:2005.00178 , year=

    On the benefits of invariance in neural networks , author=. arXiv preprint arXiv:2005.00178 , year=

    work page arXiv 2005

  22. [22]

    International Conference on Machine Learning , pages=

    Equivariant neural rendering , author=. International Conference on Machine Learning , pages=. 2020 , organization=

    work page 2020

  23. [23]

    Advances in Neural Information Processing Systems , volume=

    Unsupervised learning of group invariant and equivariant representations , author=. Advances in Neural Information Processing Systems , volume=

    work page

  24. [24]

    International conference on machine learning , pages=

    Group equivariant convolutional networks , author=. International conference on machine learning , pages=. 2016 , organization=

    work page 2016

  25. [25]

    Advances in neural information processing systems , volume=

    General e (2)-equivariant steerable cnns , author=. Advances in neural information processing systems , volume=

    work page

  26. [26]

    International Conference on Machine Learning , pages=

    Pdo-econvs: Partial differential operator based equivariant convolutions , author=. International Conference on Machine Learning , pages=. 2020 , organization=

    work page 2020

  27. [27]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=

    Fourier series expansion based filter parametrization for equivariant convolutions , author=. IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=. 2022 , publisher=

    work page 2022

  28. [28]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=

    Rotation equivariant proximal operator for deep unfolding methods in image restoration , author=. IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=. 2024 , publisher=

    work page 2024

  29. [29]

    Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pages=

    Learning steerable filters for rotation equivariant cnns , author=. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pages=

    work page

  30. [30]

    Inverse Problems , volume=

    Equivariant neural networks for inverse problems , author=. Inverse Problems , volume=. 2021 , publisher=

    work page 2021

  31. [31]

    Proceedings of the IEEE conference on computer vision and pattern recognition workshops , pages=

    Ntire 2017 challenge on single image super-resolution: Dataset and study , author=. Proceedings of the IEEE conference on computer vision and pattern recognition workshops , pages=

    work page 2017

  32. [32]

    2015 International Joint Conference on Neural Networks (IJCNN) , pages=

    Deep convolutional neural networks as generic feature extractors , author=. 2015 International Joint Conference on Neural Networks (IJCNN) , pages=. 2015 , organization=

    work page 2015

  33. [33]

    Advances in Neural Information Processing Systems , volume=

    Approximation-generalization trade-offs under (approximate) group equivariance , author=. Advances in Neural Information Processing Systems , volume=

    work page

  34. [34]

    Optimization , volume=

    Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions , author=. Optimization , volume=. 2022 , publisher=

    work page 2022

  35. [35]

    2013 , publisher=

    Perturbation analysis of optimization problems , author=. 2013 , publisher=

    work page 2013

  36. [36]

    2020 International Joint Conference on Neural Networks (IJCNN) , pages=

    General fair empirical risk minimization , author=. 2020 International Joint Conference on Neural Networks (IJCNN) , pages=. 2020 , organization=

    work page 2020

  37. [37]

    arXiv preprint arXiv:2110.03336 , year=

    Frame averaging for invariant and equivariant network design , author=. arXiv preprint arXiv:2110.03336 , year=

    work page arXiv

  38. [38]

    Advances in Neural Information Processing Systems , volume=

    A pac-bayesian generalization bound for equivariant networks , author=. Advances in Neural Information Processing Systems , volume=

    work page

  39. [39]

    Compressed sensing and its applications: third international MATHEOn conference 2017 , pages=

    Generalization error in deep learning , author=. Compressed sensing and its applications: third international MATHEOn conference 2017 , pages=. 2019 , organization=

    work page 2017

  40. [40]

    A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks

    A pac-bayesian approach to spectrally-normalized margin bounds for neural networks , author=. arXiv preprint arXiv:1707.09564 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  41. [41]

    Proceedings of the IEEE conference on computer vision and pattern recognition , pages=

    Residual dense network for image super-resolution , author=. Proceedings of the IEEE conference on computer vision and pattern recognition , pages=

    work page

  42. [42]

    Proceedings of the European conference on computer vision (ECCV) , pages=

    Image super-resolution using very deep residual channel attention networks , author=. Proceedings of the European conference on computer vision (ECCV) , pages=

    work page

  43. [43]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , year=

    Rotation equivariant arbitrary-scale image super-resolution , author=. IEEE Transactions on Pattern Analysis and Machine Intelligence , year=

    work page

  44. [44]

    Proceedings of the IEEE conference on computer vision and pattern recognition workshops , pages=

    Ntire 2017 challenge on single image super-resolution: Methods and results , author=. Proceedings of the IEEE conference on computer vision and pattern recognition workshops , pages=

    work page 2017

  45. [45]

    Proceedings of the IEEE conference on computer vision and pattern recognition , pages=

    Single image super-resolution from transformed self-exemplars , author=. Proceedings of the IEEE conference on computer vision and pattern recognition , pages=

    work page

  46. [46]

    Proceedings Eighth IEEE International Conference on Computer Vision

    A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics , author=. Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001 , volume=. 2001 , organization=

    work page 2001

  47. [47]

    International conference on curves and surfaces , pages=

    On single image scale-up using sparse-representations , author=. International conference on curves and surfaces , pages=. 2010 , organization=

    work page 2010

  48. [48]

    2012 , publisher=

    Low-complexity single-image super-resolution based on nonnegative neighbor embedding , author=. 2012 , publisher=

    work page 2012

  49. [49]

    and Garbin, Stephan J

    Worrall, Daniel E. and Garbin, Stephan J. and Turmukhambetov, Daniyar and Brostow, Gabriel J. , title =. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , month =

    work page

  50. [50]

    International journal of aeronautical and space sciences , volume=

    Satellite imagery super-resolution using squeeze-and-excitation-based GAN , author=. International journal of aeronautical and space sciences , volume=. 2021 , publisher=

    work page 2021

  51. [51]

    IEEE Geoscience and remote sensing letters , volume=

    Deep learning based feature selection for remote sensing scene classification , author=. IEEE Geoscience and remote sensing letters , volume=. 2015 , publisher=

    work page 2015

  52. [52]

    Information Fusion , volume=

    Ada4DIR: An adaptive model-driven all-in-one image restoration network for remote sensing images , author=. Information Fusion , volume=. 2025 , publisher=

    work page 2025

  53. [53]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    A model-driven deep neural network for single image rain removal , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    work page

  54. [54]

    IEEE transactions on pattern analysis and machine intelligence , volume=

    Joint rain detection and removal from a single image with contextualized deep networks , author=. IEEE transactions on pattern analysis and machine intelligence , volume=. 2019 , publisher=

    work page 2019

  55. [55]

    Proceedings of the IEEE international conference on computer vision , pages=

    Removing rain from a single image via discriminative sparse coding , author=. Proceedings of the IEEE international conference on computer vision , pages=

    work page

  56. [56]

    Proceedings of the IEEE international conference on computer vision , pages=

    Joint convolutional analysis and synthesis sparse representation for single image layer separation , author=. Proceedings of the IEEE international conference on computer vision , pages=

    work page

  57. [57]

    IEEE Transactions on Image Processing , volume=

    Clearing the skies: A deep network architecture for single-image rain removal , author=. IEEE Transactions on Image Processing , volume=. 2017 , publisher=

    work page 2017

  58. [58]

    Proceedings of the IEEE conference on computer vision and pattern recognition , pages=

    Removing rain from single images via a deep detail network , author=. Proceedings of the IEEE conference on computer vision and pattern recognition , pages=

    work page

  59. [59]

    Proceedings of the European conference on computer vision (ECCV) , pages=

    Recurrent squeeze-and-excitation context aggregation net for single image deraining , author=. Proceedings of the European conference on computer vision (ECCV) , pages=

    work page

  60. [60]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    Progressive image deraining networks: A better and simpler baseline , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    work page

  61. [61]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    Spatial attentive single-image deraining with a high quality real rain dataset , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    work page

  62. [62]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    Semi-supervised transfer learning for image rain removal , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    work page

  63. [63]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=

    Image de-raining transformer , author=. IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=. 2022 , publisher=

    work page 2022

  64. [64]

    Advances in neural information processing systems , volume=

    Imagenet classification with deep convolutional neural networks , author=. Advances in neural information processing systems , volume=

    work page

  65. [65]

    International conference on machine learning , pages=

    A convergence theory for deep learning via over-parameterization , author=. International conference on machine learning , pages=. 2019 , organization=

    work page 2019

  66. [66]

    Neural networks , volume=

    Multilayer feedforward networks are universal approximators , author=. Neural networks , volume=. 1989 , publisher=

    work page 1989

  67. [67]

    Uncertainty in artificial intelligence , pages=

    Improved generalization bounds of group invariant/equivariant deep networks via quotient feature spaces , author=. Uncertainty in artificial intelligence , pages=. 2021 , organization=

    work page 2021

  68. [68]

    Surveys in combinatorics , volume=

    On the method of bounded differences , author=. Surveys in combinatorics , volume=. 1989 , publisher=

    work page 1989

  69. [69]

    Image-to-Image Translation Framework Embedded with Rotation Symmetry Priors

    Image-to-Image Translation Framework Embedded with Rotation Symmetry Priors , author=. arXiv preprint arXiv:2604.12805 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  70. [70]

    European conference on computer vision , pages=

    KXNet: A model-driven deep neural network for blind super-resolution , author=. European conference on computer vision , pages=. 2022 , organization=

    work page 2022