SBL-based multi-task algorithms for recovering block-sparse signals with unknown partitions

Ying-Gui Wang,Zheng Liu,Wen-Li Jiang,Le Yang

doi:10.1186/1687-6180-2014-14

Abstract

We consider in this paper the problem of reconstructing block-sparse signals with unknown block partitions. In the first part of this work, we extend the block-sparse Bayesian learning (BSBL) originally developed for recovering a single block-sparse signal in a single compressive sensing (CS) task scenario to the case of multiple CS tasks. A new multi-task signal recovery algorithm, called the extended multi-task block-sparse Bayesian learning (EMBSBL), is proposed. EMBSBL exploits the statistical correlation among multiple signals as well as the intra-block correlation within individual signals to improve performance. Besides, it does not need a priori information on block partition. As the second part of this paper, we develop the EMBSBL-based synthesized multi-task signal recovery algorithm, namely SEMBSBL, to make it applicable to the single CS task case. The idea is to synthesize new CS tasks from the single CS task via circular-shifting operations and utilizes the minimum description length principle to determine the proper set of the synthesized CS tasks for signal reconstruction. SEMBSBL can achieve better signal reconstruction performance over other algorithms that recover block-sparse signals individually. Simulations corroborate the theoretical developments.

Highlights

Compressive sensing (CS) enables reconstructing a signal that is sparse in a certain domain from its measurements obtained at a rate significantly lower than the Nyquist frequency [1]
We study the impact of different signal intercorrelation levels on the signal recovery performance of extended multi-task block-sparse Bayesian learning (EMBSBL)
We find that EMBSBL can recover the original signals with reduced signal reconstruction error as the inter-correlation among original signals increases

Summary

Introduction

Compressive sensing (CS) enables reconstructing a signal that is sparse in a certain domain from its measurements obtained at a rate significantly lower than the Nyquist frequency [1]. We shall generalize EBSBL to the MCS scenario and obtain a new technique, referred to as extended multi-task blocksparse Bayesian learning (EMBSBL). When there is only one CS task, the proposed EMBSBL algorithm would become inapplicable To address this problem, in the second part of this work, we shall augment EMBSBL with the concept of the synthesized multi-taskbased signal recovery. SEMBSBL first synthesizes multiple CS tasks from the single-task CS and applies EMBSBL to recover the block-sparse signal. With increase in the computational complexity, the newly proposed SEMBSBL technique outperforms the previously developed block-sparse signal recovery methods in terms of significantly reduced reconstruction errors and the removal of the needs for detailed information on the sparsity structure.

Estimating γ

EMBSBL

Synthesis of multiple CS tasks

Simulations

Findings

Conclusion