# A Regularization-Guided Equivariant Approach for Image Restoration

arXiv: https://arxiv.org/abs/2505.19799 · HTML: https://mlsanity.com/paper/2505.19799/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 52 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Understanding Neural Networks Through Deep Visualization](https://mlsanity.com/paper/1506.06579/) (2015)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Progressive Image Deraining Networks: A Better and Simpler Baseline](https://mlsanity.com/paper/1901.09221/) (2019)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Recurrent Squeeze-and-Excitation Context Aggregation Net for Single Image Deraining](https://mlsanity.com/paper/1807.05698/) (2018)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Spatial Attentive Single-Image Deraining with a High Quality Real Rain Dataset](https://mlsanity.com/paper/1904.01538/) (2019)
- [Clearing the Skies: A deep network architecture for single-image rain removal](https://mlsanity.com/paper/1609.02087/) (2016)
- [A Model-driven Deep Neural Network for Single Image Rain Removal](https://mlsanity.com/paper/2005.01333/) (2020)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [Equivariant Multi-Modality Image Fusion](https://mlsanity.com/paper/2305.11443/) (2023)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Oriented Response Networks](https://mlsanity.com/paper/1701.01833/) (2017)
- [DuDoNet: Dual Domain Network for CT Metal Artifact Reduction](https://mlsanity.com/paper/1907.00273/) (2019)
- [TI-POOLING: transformation-invariant pooling for feature learning in Convolutional Neural Networks](https://mlsanity.com/paper/1604.06318/) (2016)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [Deep Learning to Segment Pelvic Bones: Large-scale CT Datasets and Baseline Models](https://mlsanity.com/paper/2012.08721/) (2020)
- [Deep Lesion Graphs in the Wild: Relationship Learning and Organization of Significant Radiology Image Findings in a Diverse Large-scale Lesion Database](https://mlsanity.com/paper/1711.10535/) (2017)
- [Relaxing Equivariance Constraints with Non-stationary Continuous Filters](https://mlsanity.com/paper/2204.07178/) (2022)
- [Deep Sinogram Completion with Image Prior for Metal Artifact Reduction in CT Images](https://mlsanity.com/paper/2009.07469/) (2020)
- [PDO-eConvs: Partial Differential Operator Based Equivariant Convolutions](https://mlsanity.com/paper/2007.10408/) (2020)
- [Revisiting Spatial Invariance with Low-Rank Local Connectivity](https://mlsanity.com/paper/2002.02959/) (2020)

## Built on by (most cited first, 5 of 5)

- [Scaling Laws and Symmetry, Evidence from Neural Force Fields](https://mlsanity.com/paper/2510.09768/) (2025)
- [Approximate Equivariance via Projection-based Regularisation](https://mlsanity.com/paper/2601.05028/) (2026)
- [Rotation Equivariant Mamba for Vision Tasks](https://mlsanity.com/paper/2603.09138/) (2026)
- [Implicit Augmentation from Distributional Symmetry in Turbulence Super-Resolution](https://mlsanity.com/paper/2509.20683/) (2025)
- [RoES: Rotational Equivariant Selective-frequency Fusion for Multimodal Images](https://mlsanity.com/paper/2609.12497/) (2026)

## Abstract (arXiv)

Equivariant and invariant deep learning models have been developed to exploit intrinsic symmetries in data, demonstrating significant effectiveness in certain scenarios. However, these methods often suffer from limited representation accuracy and rely on strict symmetry assumptions that may not hold in practice. These limitations pose a significant drawback for image restoration tasks, which demands high accuracy and precise symmetry representation. To address these challenges, we propose a rotation-equivariant regularization strategy that adaptively enforces the appropriate symmetry constraints on the data while preserving the network's representational accuracy. Specifically, we introduce EQ-Reg, a regularizer designed to enhance rotation equivariance, which innovatively extends the insights of data-augmentation-based and equivariant-based methodologies. This is achieved through self-supervised learning and the spatial rotation and cyclic channel shift of feature maps deduce in the equivariant framework. Our approach firstly enables a non-strictly equivariant network suitable for image restoration, providing a simple and adaptive mechanism for adjusting equivariance based on task. Extensive experiments across three low-level tasks demonstrate the superior accuracy and generalization capability of our method, outperforming state-of-the-art approaches.