Equivariant Deep Equilibrium Models for Imaging Inverse Problems

TL;DR

This paper introduces equivariant deep equilibrium models for imaging inverse problems, leveraging signal symmetries to improve reconstruction without ground truth, and simplifies training through modular backpropagation.

Contribution

It presents a novel approach combining equivariant imaging with deep equilibrium models, simplifying training and demonstrating superior performance.

Findings

DEQs trained with implicit differentiation outperform Jacobian-free methods

EI-trained DEQs approximate the proximal map of an invariant prior

Modular backpropagation simplifies the training process

Abstract

Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed point of a learned operator. However, training DEQs with complex EI losses requires implicit differentiation through fixed-point computations, whose implementation can be challenging. We show that backpropagation can be implemented modularly, simplifying training. Experiments demonstrate that DEQs trained with implicit differentiation outperform those trained with Jacobian-free backpropagation and other baseline methods. Additionally, we find evidence that EI-trained DEQs approximate the proximal map of an invariant prior.