Iterative Forward-Backward Pursuit Algorithm for Compressed Sensing

Jianping Zhang,Tianyu Geng,Guiling Sun,Feng Wang

doi:10.1155/2016/5940371

Abstract

It has been shown that iterative reweighted strategies will often improve the performance of many sparse reconstruction algorithms. Iterative Framework for Sparse Reconstruction Algorithms (IFSRA) is a recently proposed method which iteratively enhances the performance of any given arbitrary sparse reconstruction algorithm. However, IFSRA assumes that the sparsity level is known. Forward-Backward Pursuit (FBP) algorithm is an iterative approach where each iteration consists of consecutive forward and backward stages. Based on the IFSRA, this paper proposes the Iterative Forward-Backward Pursuit (IFBP) algorithm, which applies the iterative reweighted strategies to FBP without the need for the sparsity level. By using an approximate iteration strategy, IFBP gradually iterates to approach the unknown signal. Finally, this paper demonstrates that IFBP significantly improves the reconstruction capability of the FBP algorithm, via simulations including recovery of random sparse signals with different nonzero coefficient distributions in addition to the recovery of a sparse image.

Highlights

Compressed Sensing (CS) is a new paradigm in signal processing which was put forward by [1, 2]
This paper proposes the Iterative Forward-Backward Pursuit (IFBP) algorithm to further enhance the performance of Forward-Backward Pursuit (FBP) by using the iterative framework
Combining FBP with Iterative Framework for Sparse Reconstruction Algorithms (IFSRA), this paper proposes IFBP algorithm

Summary

Introduction

Compressed Sensing (CS) is a new paradigm in signal processing which was put forward by [1, 2]. Many algorithms have been proposed to solve this problem, which seems to be intractable They can be roughly divided into three categories: Greedy Pursuit, Convex Relaxation, and Bayesian Framework. Greedy methods iteratively identify elements of the estimated support set At last, these methods use a simple least-square to recover the original signal. These methods use a simple least-square to recover the original signal They mainly include Matching Pursuit (MP) algorithm [3], Orthogonal Matching Pursuit (OMP) [4], Subspace Pursuit (SP) [5], Compressive Sampling MP (CoSaMP) [6], Look Ahead OMP (LAOMP) [7], and Forward-Backward Pursuit (FBP) [8]. By inheriting the iterative idea of IFSRA, this paper proposes the Iterative Forward-Backward Pursuit (IFBP) algorithm.

Compressed Sensing and Reconstruction Algorithm

Iterative Forward-Backward Pursuit

Experimental Evaluation

Findings

Conclusions