压缩感知中迂回式匹配追踪算法

发布时间：2018-03-05 15:33

本文选题：压缩感知　切入点：贪婪算法　出处：《计算机研究与发展》2014年09期 　论文类型：期刊论文

【摘要】：迂回式匹配追踪(detouring matching pursuit,DMP)是一种计算复杂度低、准确率高、对传感矩阵列相关性要求低的贪婪重构稀疏信号算法.DMP中子内积逆和系数矩阵递增递减核心式被提出并证明,DMP利用子内积逆和系数矩阵减少残差误差变化量的计算量,达到降低计算复杂度的目的.另外,DMP采用先逐个最优缩减、后逐个最优扩增假定支撑集元素的方法提高重构准确率和扩大重构稀疏信号的稀疏度范围.DMP算法复杂度分析表明,DMP算法中获取、缩减和扩增假定支撑集的复杂度分别为O(K2 N),O(b(K-b)N)和O(b(K-b)N).加权间接重构0-1稀疏信号实验结果表明,对于稀疏度为M/2的0-1稀疏信号,DMP、逐步贪婪追踪(greedy pursuit algorithm,GPA)、子空间追踪(subspace pursuit,SP)、压缩采样追踪(compressive sampling matching pursuit,CoSaMP)、正交匹配追踪(orthogonal matching pursuit,OMP)的重构准确率分别为99%,65%,0%,0%和13%.非零值服从正态分布的稀疏信号实验结果也表明DMP的重构准确率优势显著.
[Abstract]:Detachable matching tracking (DMP) is a low computational complexity and high accuracy. Greedy reconstruction sparse signal algorithm. DMP inner product inverse and coefficient matrix decreasing kernel formula which require low correlation to sensor matrix column are proposed and proved that DMP can reduce the amount of residual error change by using subinner product inverse and coefficient matrix. The purpose of reducing computational complexity is achieved. In addition, DMP is reduced one by one. The method of increasing the reconstruction accuracy and enlarging the sparse range of the reconstructed signal. The complexity analysis of the DMP algorithm shows that the DMP algorithm can be obtained from the DMP algorithm. The complexity of reduced and expanded supposition support sets is OFK _ 2N ~ (K ~ (+)) and O _ (B) K _ (B) N _ (N) respectively. The experimental results of weighted indirect reconstruction of 0-1 sparse signals show that, For 0-1 sparse signal with m / 2 sparsity, the reconstruction accuracy of greedy pursuit algorithm, subspace subspace pursuitto, compressed sampling tracking compressing sampling matching pursuitto CoSaMPI, orthogonal matching tracking orthogonal matching suitOMP) are 9965650% and 13.3%, respectively. The non-zero value is from normal distribution. The experimental results of sparse signal of DMP also show that the reconstruction accuracy of DMP is significant.
【作者单位】：湘潭大学信息工程学院;智能计算与信息处理教育部重点实验室(湘潭大学);国防科学技术大学计算机学院;
【基金】：国家自然科学基金项目(61372049,61379115,61100215,61311140261,61070180) 湖南省自然科学基金项目(13JJ8006,12JJ9021) 湖南省科技厅科技计划项目(2011GK3200) 湖南省重点学科建设项目
【分类号】：TN911.7

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