A Regularization-Guided Equivariant Approach for Image Restoration

TL;DR

This paper introduces EQ-Reg, a rotation-equivariant regularizer that adaptively enforces symmetry constraints in deep learning models, significantly improving image restoration accuracy and generalization by balancing equivariance and representational precision.

Contribution

The paper proposes a novel adaptive regularization strategy, EQ-Reg, that enhances rotation equivariance in neural networks for image restoration, overcoming limitations of strict symmetry assumptions.

Findings

Outperforms state-of-the-art methods in three low-level image tasks.

Enhances model accuracy and generalization through adaptive equivariance.

Provides a simple, self-supervised mechanism for symmetry enforcement.

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.