Bernoulli-Gaussian Approximate Message-Passing Algorithm for Compressed Sensing with 1D-Finite-Difference Sparsity

TL;DR

This paper introduces ssAMP-BGFD, a fast and efficient approximate message-passing algorithm tailored for compressed sensing problems with 1D-finite-difference sparsity, achieving near state-of-the-art performance.

Contribution

The paper presents a novel low-computational AMP algorithm using Bernoulli-Gaussian prior for 1D-finite-difference sparse signals, with an EM-based parameter learning method.

Findings

Nearly approaches state-of-the-art phase transition performance

Exhibits fast convergence and low CPU runtime

Outperforms recent algorithms in empirical tests

Abstract

This paper proposes a fast approximate message-passing (AMP) algorithm for solving compressed sensing (CS) recovery problems with 1D-finite-difference sparsity in term of MMSE estimation. The proposed algorithm, named ssAMP-BGFD, is low-computational with its fast convergence and cheap per-iteration cost, providing phase transition nearly approaching to the state-of-the-art. The proposed algorithm is originated from a sum-product message-passing rule, applying a Bernoulli-Gaussian (BG) prior, seeking an MMSE solution. The algorithm construction includes not only the conventional AMP technique for the measurement fidelity, but also suggests a simplified message-passing method to promote the signal sparsity in finite-difference. Furthermore, we provide an EM-tuning methodology to learn the BG prior parameters, suggesting how to use some practical measurement matrices satisfying the RIP requirement under the ssAMP-BGFD recovery. Extensive empirical results confirms performance of the proposed algorithm, in phase transition, convergence speed, and CPU runtime, compared to the recent algorithms.