A Hybrid Orthogonal Forward-Backward Pursuit Algorithm for Partial Fourier Multiple Measurement Vectors Problem

Haiqiang Liu,Hongsheng Yin,Yonggang Xu,Aichun Zhu,Gang Hua

doi:10.1155/2018/5965020

Abstract

In solving the partial Fourier Multiple Measurement Vectors (FMMV) problem, existing greedy pursuit algorithms such as Simultaneous Orthogonal Matching Pursuit (SOMP), Simultaneous Subspace Pursuit (SSP), Hybrid Matching Pursuit (HMP), and Forward-Backward Pursuit (FBP) suffer from low recovery ability or need sparsity as a prior information. This paper combines SOMP and FBP to propose a Hybrid Orthogonal Forward-Backward Pursuit (HOFBP) algorithm. As an iterative algorithm, each iteration of HOFBP consists of two stages. In the first stage, α indices selected by SOMP are added to the support set. In the second stage, the support set is shrank by removing β indices. The choice of α and β is critical to the performance of this algorithm. The simulation results showed that, by using proper parameters, HOFBP has better performance than other greedy pursuit algorithms at the expense of more computing time in some cases. HOFBP does not need sparsity as a prior knowledge.

Highlights

Compressed Sensing (CS) [1,2,3] is a new information collection theory which has broken through the Nyquist sampling theorem
It is known that the greedy pursuit (GP) algorithms are based on the iterative selection of the strongest components in the measurements projected onto the measurement matrix columns
Greedy pursuit (GP) algorithms have some problems in solving the partial Fourier Measurement Vector (MMV) problem

Summary

Introduction

Compressed Sensing (CS) [1,2,3] is a new information collection theory which has broken through the Nyquist sampling theorem. J. Burkholder [17] combine SOMP and SSP to propose the Hybrid Matching Pursuit (HMP) algorithm. Forward-Backward Pursuit (FBP) [23] does not need the sparsity constraint as a prior information. It is weak in distinguishing adjoining atoms. We combine SOMP and FBP to propose a Hybrid Orthogonal Forward-Backward Pursuit (HOFBP) algorithm. Inheriting the advantages of both SOMP and FBP, HOFBP has high-resolution in distinguishing adjoining atoms, as well as a mechanism to revaluate the selected indices, and does not require sparsity as a prior information.

Notation and Concepts

Greedy Pursuit Algorithms

Computational Complexity Analysis

Simulation Results and Analysis

Conclusion