Onsager-corrected deep learning for sparse linear inverse problems

TL;DR

This paper introduces a new neural network architecture inspired by the Onsager correction in AMP algorithms, significantly improving sparse signal recovery in compressive sensing tasks over previous learned iterative methods.

Contribution

The paper proposes a novel Onsager-corrected neural network architecture for sparse linear inverse problems, enhancing accuracy and efficiency compared to prior learned iterative algorithms.

Findings

Learned AMP network outperforms learned ISTA in accuracy.

The architecture improves recovery with lower complexity.

Numerical experiments validate the effectiveness of the approach.

Abstract

Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem encountered in compressive sensing, where one seeks to recover a sparse signal from a small number of noisy linear measurements. In this paper, we propose a novel neural-network architecture that decouples prediction errors across layers in the same way that the approximate message passing (AMP) algorithm decouples them across iterations: through Onsager correction. Numerical experiments suggest that our "learned AMP" network significantly improves upon Gregor and LeCun's "learned ISTA" network in both accuracy and complexity.