Computationally Efficient Sparse Bayesian Learning via Generalized Approximate Message Passing

TL;DR

This paper introduces a computationally efficient sparse Bayesian learning algorithm that leverages generalized approximate message passing within an EM framework, significantly reducing complexity for large-scale sparse signal recovery.

Contribution

The paper presents a novel sparse Bayesian learning method using GAMP to approximate posteriors efficiently, enabling practical application to high-dimensional problems.

Findings

Reduces computational complexity compared to traditional methods.

Demonstrates effective sparse signal recovery in experiments.

Shows improved scalability for large data sets.

Abstract

The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless, the sparse Bayesian learning algorithm has computational complexity that grows exponentially with the dimension of the signal, which hinders its application to many practical problems even with moderately large data sets. To address this issue, in this paper, we propose a computationally efficient sparse Bayesian learning method via the generalized approximate message passing (GAMP) technique. Specifically, the algorithm is developed within an expectation-maximization (EM) framework, using GAMP to efficiently compute an approximation of the posterior distribution of hidden variables. The hyperparameters associated with the hierarchical Gaussian prior are learned by iteratively maximizing the Q-function which is calculated based on the posterior approximation obtained from the GAMP. Numerical results are provided to illustrate the computational efficacy and the effectiveness of the proposed algorithm.