基于SVD-Schmidt正交化的压缩感知测量矩阵的优化  

Optimization of compressed sensing measurement matrix based on SVD-Schmidt orthogonalization

作　　者：王月 覃亚丽[1] WANG Yue;QIN Yali(College of Information Engineering,Zhejiang University of Technology,Hangzhou 310023)

机构地区：[1]浙江工业大学信息工程学院,杭州310023

出　　处：《高技术通讯》2024年第10期1046-1057,共12页Chinese High Technology Letters

基　　金：国家自然科学基金(61675184)资助项目。

摘　　要：压缩感知(CS)理论中测量矩阵的性能优劣直接影响信号重构性能。为了优化测量矩阵提高其重构性能,本文提出了一种基于奇异值分解-施密特(SVD-Schmidt)正交化的CS测量矩阵优化方法。首先对测量矩阵进行奇异值分解(SVD)并选择最大的奇异值替换原来的奇异值形成新的矩阵,同时对其进行施密特正交化,对矩阵的列进行单位化,通过行和列不断循环交替自适应迭代优化得到优化后的测量矩阵。通过一维信号和二维图像的仿真实验验证所提方法的优越性。一方面,本文方法优化的测量矩阵互相关性明显降低;另一方面,实验仿真结果证明了测量矩阵经过优化之后提高了信号重构性能,本文方法重构性能优于现有的SVD法和特征值分解法。The performance of measurement matrices in compressed sensing(CS)theory affects the signal reconstruction performance.In order to optimize the measurement matrix and improve its reconstruction performance,this paper proposes an optimization method of CS measurement matrix based on singular value decomposition-Schmidt(SVDSchmidt)orthogonalization.Singular value decomposition(SVD)of the measurement matrix is performed and the largest singular value is selected to replace original singular values to form a new matrix,and Schmidt normalization of it is performed,columns of the matrix are unitized.The optimization measurement matrix is obtained by the adaptive iterative optimization of rows and columns.The superiority of the proposed method is verified by simulation experiments of one-dimensional signal and two-dimensional image.The proposed optimization measurement matrix reduces the coherence obviously.Furthermore,the simulation results show that the signal reconstruction performance is improved after optimizing the measurement matrix,and the reconstruction performance of the proposed method is better than that of the existing SVD method and eigenvalue decomposition method.

关 键 词：压缩感知(CS) 测量矩阵 互相关性 奇异值分解-施密特(SVD-Schmidt)正交化 迭代优化 

分 类 号：TN911.7[电子电信—通信与信息系统]