任意稀疏结构的多量测向量快速稀疏重构算法研究

doi:10.3969/j.issn.0372-2112.2015.04.012

电子学报 ›› 2015, Vol. 43 ›› Issue (4): 708-715.DOI: 10.3969/j.issn.0372-2112.2015.04.012

任意稀疏结构的多量测向量快速稀疏重构算法研究

李少东¹, 陈文峰¹, 杨军², 马晓岩²

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

收稿日期:2014-01-03 修回日期:2014-07-10 出版日期:2015-04-25
- 作者简介:
- 李少东 男,1987年出生于河北保定.空军预警学院博士生.主要研究方向为压缩感知在ISAR中的应用、雷达成像.E-mail:liying198798@126.com;陈文峰 男,1989年出生于新疆伊犁.空军预警学院硕士生.主要研究方向为雷达成像、压缩感知.E-mail:chenwf925@163.com;杨军男,1973年出生于云南大理.空军预警学院副教授、硕士生导师.主要研究方向为雷达系统、雷达信号处理与检测理、SAR/ISAR成像等.马晓岩男,1962年出生于湖北赤壁.空军预警学院教授、博士生导师,主要研究方向为雷达系统、雷达信号处理与检测理、现代信号处理及其应用.
- 基金资助:
- 军队重点项目

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

LI Shao-dong¹, CHEN Wen-feng¹, YANG Jun², MA Xiao-yan²

1. Department of Graduate Management, Air Force Early Warning Academy, Wuhan, Hubei 430019, China;
2. Department of Air/Space Early Warning Equipment, Air Force Early Warning Academy, Wuhan, Hubei 430019, China

Received:2014-01-03 Revised:2014-07-10 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

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.

关键词: 稀疏重构, 任意稀疏结构, 多量测向量, 贝叶斯组检验, 矩阵平滑零范数法

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.

Key words: sparse recovery, arbitrary sparse structure, multiple measurement vectors, Bayesian group testing, matrix smoothed L0-norm

中图分类号:

TN911.7

李少东, 陈文峰, 杨军, 马晓岩. 任意稀疏结构的多量测向量快速稀疏重构算法研究[J]. 电子学报, 2015, 43(4): 708-715.

LI Shao-dong, CHEN Wen-feng, YANG Jun, MA Xiao-yan. Study on the Fast Sparse Recovery Algorithm via Multiple Measurement Vectors of Arbitrary Sparse Structure[J]. Acta Electronica Sinica, 2015, 43(4): 708-715.

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任意稀疏结构的多量测向量快速稀疏重构算法研究

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

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