基于奇异值分解的测量矩阵优化  

Optimized Measurement Matrix Based on Singular Value Decomposition

作　　者：张成[1,2] 欧书琴 沈川[1] 韦穗[1] 韩超[4] 夏云[5] 

机构地区：[1]安徽大学计算智能与信号处理教育部重点实验室,安徽合肥230039 [2]安徽省现代成像与显示技术重点实验室,安徽合肥230039 [3]安徽轻工业技师学院,安徽合肥230601 [4]安徽工程大学电气工程学院,安徽芜湖241000 [5]安徽省地方税务局,安徽合肥230061

出　　处：《四川大学学报（工程科学版）》2016年第3期136-141,共6页Journal of Sichuan University (Engineering Science Edition)

基　　金：NSFC-广东联合基金资助项目(U1201255);国家自然科学基金资助项目(61301296;61377006;61501001);安徽省自然科学基金资助项目(1508085MF121;1608085QF161);安徽省教育厅重点项目资助(KJ2015A114);安徽大学博士科研启动经费资助项目(33190218)

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,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。该方法先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。In order to solve the problem raised in compressive sensing theory that the classical measurement matrices （random Gaussian, random Bernoulli, et al. ） does not achieve the optimal performance, a novel method was proposed for the measurement matrix optimization based on singular value decomposition. In this method, the singular value decomposition was introduced 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 was reconstructed by the optimized linear measurement model. Numerical results for the classical random Gaussian measurement matrix and random Bernoulli measurement matrix demonstrated that the proposed method can significantly increase the reconstruction probability of successful recovery and is more robust to Gaussian noise and applicable to the general linear measurement system ,which can successfully achieve the separation of the measurement matrix and the reconstruction matrix, and make the reconstrnction matrix close to the most excellent configuration without the any model change at the front end of the measurement system.

关 键 词：压缩感知 稀疏性 测量矩阵 重建矩阵 奇异值分解 

分 类 号：TN911.7[电子电信—通信与信息系统]