Efficient High-Dimensional Inference in the Multiple Measurement Vector Problem

TL;DR

This paper introduces AMP-MMV, a Bayesian approximate message passing algorithm designed for high-dimensional, noisy MMV problems in compressive sensing, exploiting temporal correlations for efficient sparse signal recovery.

Contribution

It extends approximate message passing techniques to amplitude-correlated MMV problems and integrates an EM algorithm for automatic parameter tuning.

Findings

Linear computational complexity in problem dimensions.

Effective exploitation of temporal correlations.

Demonstrated superior performance in high-dimensional settings.

Abstract

In this work, a Bayesian approximate message passing algorithm is proposed for solving the multiple measurement vector (MMV) problem in compressive sensing, in which a collection of sparse signal vectors that share a common support are recovered from undersampled noisy measurements. The algorithm, AMP-MMV, is capable of exploiting temporal correlations in the amplitudes of non-zero coefficients, and provides soft estimates of the signal vectors as well as the underlying support. Central to the proposed approach is an extension of recently developed approximate message passing techniques to the amplitude-correlated MMV setting. Aided by these techniques, AMP-MMV offers a computational complexity that is linear in all problem dimensions. In order to allow for automatic parameter tuning, an expectation-maximization algorithm that complements AMP-MMV is described. Finally, a detailed numerical study demonstrates the power of the proposed approach and its particular suitability for application to high-dimensional problems.