基于压缩感知中矩阵分解的观测矩阵改进  

Improvement of Measurement Matrix with Matrix Decomposition in Compressive Sensing

作　　者：兰明然 王友国[1] 

机构地区：[1]南京邮电大学理学院,江苏南京210046

出　　处：《计算机技术与发展》2017年第6期56-59,65,共5页Computer Technology and Development

基　　金：国家自然科学基金资助项目(61179027)

摘　　要：观测矩阵构造是压缩感知(CS)理论中的重点。在构造观测矩阵中,应尽可能地降低观测矩阵与稀疏变换基之间的相关性,同时增大观测矩阵列的独立性。为此,提出了一种新的改进方法。该方法采用梯度下降法处理Gram矩阵以降低其非对角线元素,在对所得到的观测矩阵进行QR分解的基础上,再对QR分解后的矩阵进行奇异值(SVD)分解,以进一步增大观测矩阵的列独立性。为了验证所提出算法的有效性,将所得观测矩阵分别与未优化的高斯矩阵、经SVD分解优化的高斯矩阵和梯度下降法优化的高斯矩阵在同等压缩比下进行了对比仿真实验。对比仿真实验结果表明,应用所提出算法而得到的矩阵具有较好的重构性能,特别当压缩比小于0.3时,对应于未经优化的观测矩阵,峰值信噪比提高约2至3倍。The structure of measurement matrix is the key point in the theory of Compressive Sensing （CS）. In the measurement matrix constructing, it is possible to reduce the correlation between the measurement matrix and the sparse transformation matrix, and to increase the independence of the measurement matrix. A new improved method has been proposed for this purpose, which uses gradient Gram ma- trix to reduce its non-diagonal elements with descent method of measurement matrix obtained by QR decomposition. After decomposition of the QR matrix,Singular Value Decomposition （SVD） has been implemented to further increase the independence among the measure- ment matrix. In order to verify the effectiveness of the proposed algorithm, contrast experiments of matrix acquired by the proposed meth- od with three types of Gauss matrices, such as these without optimization, optimized by SVD decomposition and optimized by gradient de- scent method, have been carried out at the same compression. The experimental simulation results show that the proposed algorithm and thus the reconstruction matrix have displayed better performance,especially when the compression ratio is less than 0.3 ,the peak signal- to-noise ratio has increased about 2 to 3 times comparing with the measurement matrix without optimization.

关 键 词：压缩感知 观测矩阵 QR分解 SVD分解 

分 类 号：TP31[自动化与计算机技术—计算机软件与理论]