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

作　　者：李少东[1] 陈文峰[1] 杨军[2] 马晓岩[2] 

机构地区：[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

出　　处：《电子学报》2015年第4期708-715,共8页Acta Electronica Sinica

基　　金：军队重点项目

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.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 LO-norm （MSLO） 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 slructure 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.

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 

分 类 号：TP911.7[自动化与计算机技术]