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工程科学与技术:2016,48(3):136-141
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基于奇异值分解的测量矩阵优化
(1.安徽大学;2.安徽轻工业技师学院;3.安徽大学计算智能与信号处理教育部重点实验室;4.安徽工程大学电气工程学院;5.安徽省地方税务局)
Optimized Measurement Matrix Based on Singular Value Decomposition
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投稿时间:2015-05-15    修订日期:2016-04-02
中文摘要: 针对压缩感知理论中通用的测量矩阵(如随机高斯、伯努利等)不具有最优性能保证的问题,本文通过引入奇异值分解,提出基于奇异值分解的测量矩阵优化方法,对压缩感知中一般线性测量模型中的测量矩阵与测量向量进行优化,再利用优化后的测量矩阵与测量向量重建原稀疏信号。经典的随机高斯测量矩阵和伯努利测量矩阵的数值实验结果表明本文提出的方法可以显著地提高重建成功恢复概率以及对高斯噪声的鲁棒性。该方法适用于一般线性测量系统,成功地实现了测量矩阵和重建矩阵的分离,可在不改变前端测量模型的前提下使重建矩阵接近最优配置。
Abstract:According the problem raised in compressive sensing theory that the classical measurement matrices (random Gaussian, random Bernoulli, etc.) does not achieve the optimal performance, the singular value decomposition is introduced in this paper, thus a novel method is proposed for the measurement matrix optimization based on singular value decomposition, to optimize the general linear measurement model in compressive sensing, i.e. measurement matrix and corresponded measurement vector, and then the original signal sparse signal is reconstructed by the optimized linear measurement model. Numerical results for the classical random Gaussian measurement matrix and random Bernoulli measurement matrix demonstrate that our proposed method can significantly increase the reconstruction probability of successful recovery and are more robust to Gaussian noise. Our proposed method is applicable to the general linear measurement system, which can successfully achieve the separation of the measurement matrix and the reconstruction matrix, and make the reconstruction matrix close to the most excellent configuration without the any model change at the front end of the measurement system.
文章编号:201500457     中图分类号:    文献标志码:
基金项目:61301296, 61377006, 61501001
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Zhang Cheng  question1996@163.com 
欧书琴   
   
   
   
   
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引用文本:
张成,欧书琴,沈川,韦穗,韩超,夏云.基于奇异值分解的测量矩阵优化[J].工程科学与技术,2016,48(3):136-141.
Zhang Cheng,欧书琴.Optimized Measurement Matrix Based on Singular Value Decomposition[J].Advanced Engineering Sciences,2016,48(3):136-141.