摘要
在压缩感知CS(Compressed Sensing)理论中,测量矩阵的构造至关重要,其性能直接影响到数据压缩采样的效率及信号的重构质量。针对Toeplitz结构测量矩阵重构性能不高的问题,提出一种基于奇异值分解的Toeplitz结构测量矩阵构造方法。首先对Toeplitz矩阵进行奇异值分解,然后通过对该矩阵的非零奇异值进行优化来提高矩阵的列向量独立性,从而提高其重构性能。仿真结果表明,相比较未优化的Toeplitz结构测量矩阵以及当前常用的高斯随机矩阵,当采用优化后的Toeplitz结构测量矩阵对信号进行压缩感知时,信号的重构精度得到显著提高。
The construction of measurement matrix is crucial to compressed sensing theory,its performance directly affects the efficiency of data sampling compression and the quality of signal reconstruction.In view of the fact that the performance of Toeplitz structure measurement matrix reconstruction is not high,we proposed a singular value decomposition-based construction method for Toeplitz structure measurement matrix.First,it decomposes the Toeplitz matrix by using singular value decomposition algorithm,then it enhances the independence of column vectors of the matrix by optimising its nonzero singular values,so as to improve the reconstruction performance.Simulation results showed that compared with the non-optimised Toeplitz structure measurement matrix and the frequently used Gauss random matrix,the signal reconstruction accuracy gained significant improvement when using the optimized Toeplitz structure measurement matrix to carry out compressed sensing on signals.
作者
赵辉
金胜杰
Zhao Hui;Jin Shengjie(Key Laboratory of Optical Communication and Networks , Chongqing University of Posts and Telecommunictions, Chongqing 400065, China)
出处
《计算机应用与软件》
CSCD
2016年第6期180-184,共5页
Computer Applications and Software
基金
国家自然科学基金项目(61271261)
重庆市科委自然科学基金项目(CSTC2012jjA40048)
关键词
压缩感知
测量矩阵
托普利兹结构
奇异值分解
信号重构
Compressed sensing
Measurement matrix
Toeplitz structure
Singular value decomposition
Signal reconstruction
