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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (1): 15-21    DOI: 10.3785/j.issn.1008-9497.2019.01.003
矩阵理论与应用     
基于共轭梯度法的感知矩阵优化方法
李昕艺, 刘三阳, 谢维
西安电子科技大学 数学与统计学院，陕西 西安710126
A novel conjugate gradient method for sensing matrix optimization for compressed sensing systems
LI Xinyi, LIU Sanyang, XIE Wei
School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
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摘要： 压缩感知理论中降低信号维数的关键问题是构造有效的测量矩阵。在已知稀疏基的情况下，基于ETF（Equiangular Tight Frame）框架的测量矩阵构造方法和稀疏信号重构过程均依赖于感知矩阵。为此，设计了一种基于共轭梯度法的感知矩阵优化方法，该方法简单易行，且所求结果的Gram矩阵与目标Gram矩阵更接近。 实验结果表明，此感知矩阵优化方法在理论分析、实际图像应用及算法有效性上均具优势。
关键词： 压缩感知;  感知矩阵优化;  ETF框架;  共轭梯度法    
Abstract: This study deals with the issue of designing the sensing matrix for a compressed sensing system. With the given dictionary, a ETF-based （Equiangular Tight Frame） measure matrix designing method use the sensing matrix rather than a measure matrix, so does the spare signal recovery process. A novel conjugate gradient method for sensing matrix optimization is proposed in this paper. The proposed method is simple, and the result is consistent with the target Gram matrix. Simulation results show the advantage of the novel sensing matrix optimization method in theoretical analysis, real image application and algorithmic effectiveness.
Key words: compressed sensing    sensing matrix optimization    ETF frame    conjugate gradient method
收稿日期: 2018-03-29 出版日期: 2019-01-25
CLC:  TP 399  
基金资助: 陕西省自然科学基础研究计划资助(2017JM1001).
作者简介: 李昕艺（1990—），ORCID：http：//orcid. org/0000-0002-2330-1100，女，博士研究生，主要从事最优化及稀疏优化研究 .
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引用本文:

李昕艺, 刘三阳, 谢维. 基于共轭梯度法的感知矩阵优化方法[J]. 浙江大学学报（理学版）, 2019, 46(1): 15-21.

LI Xinyi, LIU Sanyang, XIE Wei. A novel conjugate gradient method for sensing matrix optimization for compressed sensing systems. Journal of Zhejiang University (Science Edition), 2019, 46(1): 15-21.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.01.003    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I1/15

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