CAJ | 학술논문

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。
압축감지시일충신적신호묘술、채양화중구이론，기핵심문제포괄측량구진적선택화구조이급중구산법설계。본문수선제출감지구진멱평균렬상관성정의，진이득출측량구진적택우원칙；연후의거등각긴광가이론화특정향량근사법，제출신적측량구진구조산법，감소감지구진적멱평균렬상관성。실험결과표명，본문산법체도료강저감지구진렬상관성적목적。령외，당중구산법상동시，채용본문산법득도적측량구진비채용 Gaussian 、Elad 、Xu 화 Vahid 산법득도측량구진적중구착오솔요저。
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 .