Unitary Approximate Message Passing for Sparse Bayesian Learning

TL;DR

This paper introduces a robust and efficient unitary approximate message passing (UAMP) algorithm for sparse Bayesian learning, improving convergence and performance for various measurement matrices.

Contribution

The paper proposes a novel UAMP-based SBL algorithm that enhances robustness and efficiency over existing AMP-based methods, applicable to single and multiple measurement vector problems.

Findings

UAMP-SBL outperforms existing AMP-based algorithms in robustness.

The proposed method achieves faster convergence.

It demonstrates superior performance in diverse measurement scenarios.

Abstract

Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it does not work well for a generic measurement matrix, which may cause AMP to diverge. Damped AMP has been used for SBL to alleviate the problem at the cost of reducing convergence speed. In this work, we propose a new SBL algorithm based on structured variational inference, leveraging AMP with a unitary transformation (UAMP). Both single measurement vector and multiple measurement vector problems are investigated. It is shown that, compared to state-of-the-art AMP-based SBL algorithms, the proposed UAMP-SBL is more robust and efficient, leading to remarkably better performance.