压缩感知中的确定性随机观测矩阵构造  

Deterministic Random Measurement Matrices Construction for Compressed Sensing

作　　者：王侠[1] 王开[1] 王青云[1,2] 梁瑞宇[2] 左加阔[1] 赵力[1] 邹采荣[1] 

机构地区：[1]东南大学水声信号处理教育部重点实验室,南京210096 [2]南京工程学院通信工程学院,南京211167

出　　处：《信号处理》2014年第4期436-442,共7页Journal of Signal Processing

基　　金：国家自然科学基金(61273266;51075068);教育部博士点基金(20110092130004;20100092120012);国家博士后基金(2012M520973);江苏省自然科学基金资助项目(BK2010240)

摘　　要：目前,压缩感知中的观测矩阵设计存在两类问题:(1)随机观测矩阵不容易硬件实现;(2)基于多项式的以及基于代数曲线的确定性观测矩阵大小不能任意选择。针对上述问题,本文提出了一种用确定性随机序列来构造观测矩阵的方法,并证明了构造出的观测矩阵满足有限等距性质(Restricted Isometry Property,RIP)。仿真实验结果表明,本文设计的矩阵与高斯随机矩阵、伯努利矩阵、稀疏矩阵、混沌矩阵相比具有同样的性能。将确定性随机矩阵应用于语音信号的压缩与重构,语音质量的主客观评价均显示,确定性随机矩阵具有良好的重构性能。Currently,two types of problems exist in the design of measurement matrices in compressed sensing.One is that random measurement matrices are difficult to be realized by hardware.The other is that the size of deterministic matrices which are based on polynomials or algebraic curves cannot be arbitrary.To cope with these problems,this paper introduced a measurement matrices construction method based on deterministic random sequences.The proof that the matrices satisfy the Restricted Isometry Property （RIP） was also given in the paper.In the simulation experiments,the proposed matrices were compared with Gaussian random matrices,Bernoulli matrices,sparse matrices and chaotic matrices.Experiment results show that the matrices designed by the proposed strategy have equal performance with other popular measurement matrices.Also,deterministic random matrices were used for speech compression and reconstruction.Subjective and objective evaluation results of speech quality both show that the proposed matrices exhibit excellent performance in speech reconstruction.

关 键 词：压缩感知 观测矩阵 确定性随机序列 

分 类 号：TN912.3[电子电信—通信与信息系统]