An Approach to Complex Bayesian-optimal Approximate Message Passing

TL;DR

This paper introduces BOSSAMP, a Bayesian-optimal algorithm for complex compressed sensing that improves support detection and signal recovery by separating activity detection from value estimation, outperforming existing methods.

Contribution

The paper proposes a novel BOSSAMP algorithm with support detection schemes for complex signals, enhancing recovery accuracy in compressed sensing.

Findings

BOSSAMP outperforms AMP and BAMP in mean squared error.

Support detection accuracy is significantly improved.

Simulations validate the effectiveness of the proposed method.

Abstract

In this work we aim to solve the compressed sensing problem for the case of a complex unknown vector by utilizing the Bayesian-optimal structured signal approximate message passing (BOSSAMP) algorithm on the jointly sparse real and imaginary parts of the unknown. By introducing a latent activity variable, BOSSAMP separates the tasks of activity detection and value estimation to overcome the problem of detecting different supports in the real and imaginary parts. We complement the recovery algorithm by two novel support detection schemes that utilize the updated auxiliary variables of BOSSAMP. Simulations show the superiority of our proposed method against approximate message passing (AMP) and its Bayesian-optimal sibling (BAMP), both in mean squared error and support detection performance.