Block Sparse Bayesian Recovery with Correlated LSM Prior

Juan Zhao,Ran Tao,Tao Shan,Xia Bai,Liangtian Wan

doi:10.1155/2021/9942694

Abstract

Compressed sensing can recover sparse signals using a much smaller number of samples than the traditional Nyquist sampling theorem. Block sparse signals (BSS) with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. Utilizing the sparse structure can improve the recovery performance. In this paper, we consider recovering arbitrary BSS with a sparse Bayesian learning framework by inducing correlated Laplacian scale mixture (LSM) prior, which can model the dependence of adjacent elements of the block sparse signal, and then a block sparse Bayesian learning algorithm is proposed via variational Bayesian inference. Moreover, we present a fast version of the proposed recovery algorithm, which does not involve the computation of matrix inversion and has robust recovery performance in the low SNR case. The experimental results with simulated data and ISAR imaging show that the proposed algorithms can efficiently reconstruct BSS and have good antinoise ability in noisy environments.

Highlights

Compressed sensing (CS) [1] provides a new sampling and reconstruction paradigm, which can recover sparse signals from linear measurements:y = Φx + n, ð1Þ where Φ ∈ RM×N ðM < NÞ is the measurement matrix, y ∈ RM is the measurement vector, x ∈ RN is the sparse signal, and n ∈ RM is the additive noise
Some block recovery algorithms based on the Bayesian compressed sensing framework are presented, including block sparse Bayesian learning (BSBL) [8], Cluss-MCMC [9], model-based Bayesian CS via local beta process (MBCS-LBP) [10], and pattern-coupled sparse Bayesian learning (PC-SBL) [11]
For the block sparse signals (BSS) with unknown block information, this paper proposes a block Bayesian recovery algorithm by inducing a correlated Laplacian scale mixture (LSM) prior model, which uses the dependence between neighboring elements of the BSS

Summary

Introduction

Compressed sensing (CS) [1] provides a new sampling and reconstruction paradigm, which can recover sparse signals from linear measurements:. Some block recovery algorithms based on the Bayesian compressed sensing framework are presented, including block sparse Bayesian learning (BSBL) [8], Cluss-MCMC [9], model-based Bayesian CS via local beta process (MBCS-LBP) [10], and pattern-coupled sparse Bayesian learning (PC-SBL) [11]. In [12], Zhang et al have proposed an expectationmaximization-based variational Bayesian (EM-VB) inference method, which utilizes the Laplacian scale mixture (LSM) model as a sparse prior; i.e., it is assumed that the sparse signal obeys the Laplacian prior because the Laplacian distribution can represent sparseness well Based on this model, for the BSS with unknown block information, this paper proposes a block Bayesian recovery algorithm by inducing a correlated LSM prior model, which uses the dependence between neighboring elements of the BSS.

Signal Model

Block Bayesian Recovery Algorithms

Simulation Experiments

Conclusions