Deep Equilibrium Architectures for Inverse Problems in Imaging

TL;DR

This paper introduces a novel deep equilibrium approach for inverse imaging problems, enabling infinite iteration modeling that improves reconstruction accuracy and allows flexible trade-offs between accuracy and computation at test time.

Contribution

It presents a deep equilibrium model for inverse problems that incorporates known forward models, surpassing traditional fixed-iteration neural network methods.

Findings

Achieves higher reconstruction accuracy than state-of-the-art methods.

Allows test-time adjustment of computational budget for optimal trade-offs.

Demonstrates effectiveness across various imaging inverse problems.

Abstract

Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in training networks corresponding to more iterations; the resulting solvers cannot be run for more iterations at test time without incurring significant errors. This paper describes an alternative approach corresponding to an infinite number of iterations, yielding a consistent improvement in reconstruction accuracy above state-of-the-art alternatives and where the computational budget can be selected at test time to optimize context-dependent trade-offs between accuracy and computation. The proposed approach leverages ideas from Deep Equilibrium Models, where the fixed-point iteration is constructed to incorporate a known forward model and insights from classical optimization-based reconstruction methods.