A Construction Algorithm of Measurement Matrix with Low Power Average Column Coherence

LI Zhe-tao; PAN Tian; ZHU Geng-ming; PEI Ting-rui

doi:10.3969/j.issn.0372-2112.2014.07.017

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A Construction Algorithm of Measurement Matrix with Low Power Average Column Coherence

更新时间：2025-07-16

- A Construction Algorithm of Measurement Matrix with Low Power Average Column Coherence
- Acta Electronica Sinica Vol. 42, Issue 7, Pages: 1360-1364(2014)
- 作者机构：
  
  1. 湘潭大学信息工程学院,湖南,湘潭,411105
  2. 湘潭大学智能计算与信息处理教育部重点实验室,湖南,湘潭,411105
  3. 湖南科技大学计算机科学与工程学院,湖南,湘潭,411201
  5. 国防科学技术大学计算机学院,湖南,长沙,410073
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2014.07.017
  CLC： TP393
- Published：2014
- 稿件说明：
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LI Zhe-tao, PAN Tian, ZHU Geng-ming, et al. A Construction Algorithm of Measurement Matrix with Low Power Average Column Coherence[J]. Acta Electronica Sinica, 2014, 42(7): 1360-1364.
DOI：

LI Zhe-tao, PAN Tian, ZHU Geng-ming, et al. A Construction Algorithm of Measurement Matrix with Low Power Average Column Coherence[J]. Acta Electronica Sinica, 2014, 42(7): 1360-1364. DOI： 10.3969/j.issn.0372-2112.2014.07.017.

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.

Abstract

Compressed sensing is a theory for signal description

sampling and reconstruction

the core issues of which are selection and construction of measurement matrix as well as reconstruction algorithm.This paper firstly presents the definition of sensing 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 approximation 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 reconstruction error ratio compared with Gaussian

Elad's

Xu's

and Vahid's method with the same reconstruction algorithm.

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