低幂平均列相关性测量矩阵构造算法

摘要

压缩感知是一种新的信号描述、采样和重构理论，其核心问题包括测量矩阵的选择和构造以及重构算法设计。本文首先提出感知矩阵幂平均列相关性定义，进而得出测量矩阵的择优原则；然后依据等角紧框架理论和特征向量近似法，提出新的测量矩阵构造算法，减小感知矩阵的幂平均列相关性。实验结果表明，本文算法达到了降低感知矩阵列相关性的目的。另外，当重构算法相同时，采用本文算法得到的测量矩阵比采用 Gaussian 、Elad 、Xu 和 Vahid 算法得到测量矩阵的重构错误率要低。%Compressed sensing is a theory for signal description ,sampling and reconstruction ,the core issues of which are se-lection and construction of measurement matrix as well as reconstruction algorithm .This paper firstly presents the definition of sens-ing matrix with power average column coherence ,and gets the preferential principle of measurement matrix according to the power average column coherence ;then a construction algorithm of measurement matrix based on equiangular tight frame (ETF) and ap-proximation method of eigenvector is proposed to decrease column coherence of sensing matrix .Experimental results show that the proposed algorithm decreases the coherence of sensing matrix efficiently .Meanwhile ,the proposed algorithm obtains lower recon-struction error ratio compared with Gaussian ,Elad’s ,Xu’s ,and Vahid’s method with the same reconstruction algorithm .