A Regularization-Guided Equivariant Approach for Image Restoration

2025-05-26

AI Summary

Existing equivariant/invariant models for image restoration rely on strict symmetry assumptions, rendering them ill-suited to real-world data exhibiting symmetry deviations and leading to suboptimal representation fidelity. To address this, we propose Equivariant Regularization (EQ-Reg), the first method to integrate self-supervised learning with spatial rotation and channel-wise cyclic shifts of feature maps—enabling task-driven, dynamic equivariance control within *non-strictly* equivariant networks. EQ-Reg requires no architectural modifications; instead, it introduces a lightweight regularization term that enhances model robustness against practical symmetry perturbations. Evaluated on three fundamental vision tasks—image deblurring, super-resolution, and denoising—EQ-Reg consistently surpasses state-of-the-art methods in both accuracy and cross-dataset generalization.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Multimodal Learning
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Limited representation accuracy in equivariant deep learning models
• Strict symmetry assumptions impractical for image restoration
• Need adaptive symmetry constraints preserving network accuracy

Innovation

• Rotation-equivariant regularization strategy adaptively enforces symmetry
• EQ-Reg enhances rotation equivariance via self-supervised learning
• Non-strictly equivariant network adapts to image restoration tasks