Expectation Consistent Plug-and-Play for MRI

TL;DR

This paper introduces a novel plug-and-play method for MRI image recovery using expectation consistent approximation, enabling more predictable error statistics and improved denoiser training compared to traditional approaches.

Contribution

It develops an EC-based PnP framework that generalizes AMP, allowing for effective deep neural network denoiser training with predictable error statistics.

Findings

Enhanced MRI reconstruction quality.

More stable and predictable denoising process.

Improved convergence properties in PnP algorithms.

Abstract

For image recovery problems, plug-and-play (PnP) methods have been developed that replace the proximal step in an optimization algorithm with a call to an application-specific denoiser, often implemented using a deep neural network. Although such methods have been successful, they can be improved. For example, the denoiser is often trained using white Gaussian noise, while PnP's denoiser input error is often far from white and Gaussian, with statistics that are difficult to predict from iteration to iteration. PnP methods based on approximate message passing (AMP) are an exception, but only when the forward operator behaves like a large random matrix. In this work, we design a PnP method using the expectation consistent (EC) approximation algorithm, a generalization of AMP, that offers predictable error statistics at each iteration, from which a deep-net denoiser can be effectively trained.