An Efficient Distributed Compressed Sensing Algorithm for Decentralized Sensor Network.

Jing Liu,Guoxian Zhang,Kaiyu Huang

doi:10.3390/s17040907

Abstract

We consider the joint sparsity Model 1 (JSM-1) in a decentralized scenario, where a number of sensors are connected through a network and there is no fusion center. A novel algorithm, named distributed compact sensing matrix pursuit (DCSMP), is proposed to exploit the computational and communication capabilities of the sensor nodes. In contrast to the conventional distributed compressed sensing algorithms adopting a random sensing matrix, the proposed algorithm focuses on the deterministic sensing matrices built directly on the real acquisition systems. The proposed DCSMP algorithm can be divided into two independent parts, the common and innovation support set estimation processes. The goal of the common support set estimation process is to obtain an estimated common support set by fusing the candidate support set information from an individual node and its neighboring nodes. In the following innovation support set estimation process, the measurement vector is projected into a subspace that is perpendicular to the subspace spanned by the columns indexed by the estimated common support set, to remove the impact of the estimated common support set. We can then search the innovation support set using an orthogonal matching pursuit (OMP) algorithm based on the projected measurement vector and projected sensing matrix. In the proposed DCSMP algorithm, the process of estimating the common component/support set is decoupled with that of estimating the innovation component/support set. Thus, the inaccurately estimated common support set will have no impact on estimating the innovation support set. It is proven that under the condition the estimated common support set contains the true common support set, the proposed algorithm can find the true innovation set correctly. Moreover, since the innovation support set estimation process is independent of the common support set estimation process, there is no requirement for the cardinality of both sets; thus, the proposed DCSMP algorithm is capable of tackling the unknown sparsity problem successfully.

Highlights

Compressed sensing has received considerable attention recently and has been applied successfully in diverse fields, e.g., image processing [1], speech enhancement [2], sensor network [3,4]and radar systems [5]
We focus on the joint sparsity Model 1 (JSM-1), and such signals may arise in a sensor network where large-scale phenomena affect all sensors and local phenomena affect individual sensors
Since the innovation support set estimation process is independent of the common support set estimation process, there is no requirement for the cardinality of both sets; the proposed distributed compact sensing matrix pursuit (DCSMP) algorithm is capable of tackling the unknown sparsity problem successfully

Summary

Introduction

Compressed sensing has received considerable attention recently and has been applied successfully in diverse fields, e.g., image processing [1], speech enhancement [2], sensor network [3,4]and radar systems [5]. As an important branch of compressed sensing, distributed compressed sensing (DCS) theory [6,7] rests on a new concept called the joint sparsity of a signal ensemble. A signal ensemble is composed of different signals from the various sensors of the same scene. Three joint sparsity models (JSM) are presented in [6]: JSM-1, JSM-2 and JSM-3. In JSM-1, each signal consists of a sum of two components: a common component that is present in all of the signals and an innovation component that is unique to each signal. In JSM-2, all signals are constructed from the same sparse set of basis vectors, but with different coefficient values. JSM-3 extends JSM-1 so that the common

Objectives

Results

Discussion

Conclusion