Study on the Fast Sparse Recovery Algorithm via Multiple Measurement Vectors of Arbitrary Sparse Structure

LI Shao-dong; CHEN Wen-feng; YANG Jun; MA Xiao-yan

doi:10.3969/j.issn.0372-2112.2015.04.012

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Study on the Fast Sparse Recovery Algorithm via Multiple Measurement Vectors of Arbitrary Sparse Structure

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- Study on the Fast Sparse Recovery Algorithm via Multiple Measurement Vectors of Arbitrary Sparse Structure
- Acta Electronica Sinica Vol. 43, Issue 4, Pages: 708-715(2015)
- 作者机构：
  
  1. 空军预警学院研究生队,湖北,武汉,430019
  2. 空军预警学院空天预警装备系,湖北,武汉,430019
  3. 空军预警学院研究生队,湖北,武汉,430019
  4. 空军预警学院空天预警装备系,湖北,武汉,430019
- 作者简介：
- 基金信息：
  
  Key Military Project
- DOI：10.3969/j.issn.0372-2112.2015.04.012
  CLC： TN911.7
- Published：2015
- 稿件说明：
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LI Shao-dong, CHEN Wen-feng, YANG Jun, et al. Study on the Fast Sparse Recovery Algorithm via Multiple Measurement Vectors of Arbitrary Sparse Structure[J]. Acta Electronica Sinica, 2015, 43(4): 708-715.
DOI：

LI Shao-dong, CHEN Wen-feng, YANG Jun, et al. Study on the Fast Sparse Recovery Algorithm via Multiple Measurement Vectors of Arbitrary Sparse Structure[J]. Acta Electronica Sinica, 2015, 43(4): 708-715. DOI： 10.3969/j.issn.0372-2112.2015.04.012.

摘要

目前的稀疏重构算法求解多量测向量时存在两个问题:一是计算复杂度高;二是不能实现任意稀疏结构的多量测向量重构.为此

本文提出一种多量测向量快速重构算法.该算法首先构建矩阵平滑零范数法

实现对具有任意稀疏结构的多量测向量的重构

并获得多量测向量的初始支撑集;其次根据稀疏度与量测维度的关系

对初始支撑集进行筛选获得预选支撑集;然后采用贝叶斯组检验方式得到信号重构所需的最终支撑集;最后通过最终支撑集实现信号的重构.该算法充分利用了矩阵平滑零范数法的高效性以及贝叶斯组检验对冗余支撑集的剔除功能

不但实现了稀疏位置随机变化的多量测向量的高效重构

而且保证了算法的精度

并对噪声具有一定的鲁棒性

基于实测数据的ISAR成像实验验证了所提算法的有效性.

Abstract

The traditional Sparse Recovery (SR) algorithms are unsuitable for signal reconstruction of Multiple Measurement Vectors (MMV) for the following two reasons

one is the high computing burden

and the other is that the presented algorithms are not used to the case when MMV are arbitrary sparse structure.To solve the problems

a novel fast sparse recovery algorithm is proposed.Firstly

the Matrix Smoothed L0-norm (MSL0) algorithm is adopted to reconstruct the MMV of arbitrary sparse structure and estimate the initial support.Secondly

using the relationship between the sparse level and measurement number

the pre-selection support is obtained from choosing the initial support.Thirdly

the final support is gotten with Bayesian Group Testing (BGT) method.And finally

the MMV is reconstructed precisely via the final support.The proposed algorithm makes full use of high efficiency of the MSL0 and redundancy support elimination ability of the BGT.The algorithm can not only reconstruct MMV of arbitrary sparse structure more efficiently

but also has higher reconstructed accuracy and better robustness.ISAR imaging experiments based on real data show the validity of the proposed algorithm.

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