Sparse Estimation with the Swept Approximated Message-Passing Algorithm

TL;DR

This paper introduces a swept coefficient update scheme for Approximate Message Passing (AMP) that stabilizes convergence in challenging inference problems, achieving near-optimal performance with manageable computational costs.

Contribution

The paper presents a novel swept AMP algorithm that improves convergence stability and performance in non-ideal settings, extending AMP's applicability.

Findings

Swept AMP stabilizes convergence where standard AMP diverges.

The computational cost remains manageable for large-scale signals.

The method achieves near-theoretical performance in challenging inference tasks.

Abstract

Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in computational efficiency. However, AMP suffers from serious convergence issues in contexts that do not exactly match its assumptions. We propose a new approach to stabilizing AMP in these contexts by applying AMP updates to individual coefficients rather than in parallel. Our results show that this change to the AMP iteration can provide theoretically expected, but hitherto unobtainable, performance for problems on which the standard AMP iteration diverges. Additionally, we find that the computational costs of this swept coefficient update scheme is not unduly burdensome, allowing it to be applied efficiently to signals of large dimensionality.