Measurement-Consistent Networks via a Deep Implicit Layer for Solving Inverse Problems

TL;DR

This paper introduces a framework that enhances deep neural networks for inverse problems by incorporating a measurement-consistent implicit layer, improving reconstruction quality and robustness, especially in sensitive applications like medical imaging.

Contribution

It proposes a novel method to enforce measurement consistency in DNNs for inverse problems using an implicit layer, improving stability and detail preservation.

Findings

Significant improvements in reconstruction quality.

Enhanced robustness against minor variations.

Applicable to single-image super-resolution.

Abstract

End-to-end deep neural networks (DNNs) have become the state-of-the-art (SOTA) for solving inverse problems. Despite their outstanding performance, during deployment, such networks are sensitive to minor variations in the testing pipeline and often fail to reconstruct small but important details, a feature critical in medical imaging, astronomy, or defence. Such instabilities in DNNs can be explained by the fact that they ignore the forward measurement model during deployment, and thus fail to enforce consistency between their output and the input measurements. To overcome this, we propose a framework that transforms any DNN for inverse problems into a measurement-consistent one. This is done by appending to it an implicit layer (or deep equilibrium network) designed to solve a model-based optimization problem. The implicit layer consists of a shallow learnable network that can be integrated into the end-to-end training while keeping the SOTA DNN fixed. Experiments on single-image super-resolution show that the proposed framework leads to significant improvements in reconstruction quality and robustness over the SOTA DNNs.