【摘要】 提出了一种新的压缩感知测量矩阵,伪随机测量矩阵(PRM),并证明了PRM矩阵满足RIP条件。该矩阵利用平衡Gold序列良好的伪随机性和相关特性,使用平衡Gold伪随机序列、沃尔什-哈达码矩阵和降采样矩阵,由结构化的方法构造,能够保留高斯随机测量矩阵、伪随机测量矩阵和确定性测量矩阵的各自优点,既具有随机矩阵的良好重建性能、普适性等性质,又具有确定性测量矩阵的便于硬件实现和的低计算复杂度等特点,使得该测量矩阵的物理实现简化。针对一维电能质量信号和二维图像的压缩采样与重构实验结果表明:PRM测量矩阵对工业信号和图像信号具有较好的普适性,且重建性能优于高斯矩阵、贝努利矩阵和Toeplitz测量矩阵,在压缩比越小的情况下效果改善越明显。更多还原

【Abstract】 In this paper,we propose a new compressed sensing measurement matrix,i. e. Pseudo-random measurement( PRM) matrix,and prove that the PRM matrix satisfies restricted isometry principle( RIP). According to the features of good pseudo-randomness and correlation of balanced Gold sequence,the RPM matrix is constructed using the structured approach with balanced Gold pseudo-randomness sequence diagonal matrix,Walsh-Hadamard matrix,and down-sampling matrix,which can retain the respective advantages of Gaussian random measurement matrix,pseudorandomness measurement matrix and deterministic measurement matrix. So,the PRM matrix not only has the good reconstruction performance and universality of random measurement matrices,but also has the characteristics of easyhardware implementation and low computing complexity of deterministic measurement matrices,which simplifies the physical implementation of the PRM matrix. The compressed sampling and reconstruction experiment results of 1D power quality signals and 2D images show that the PRM matrix has good universality for the applications of industrial signals and image signals. Furthermore,the reconstruction performance of the PRM matrix is better than those of Gaussian matrix,Bernoulli matrix and Toeplitz measurement matrix,and the less the compression ratio is,the better the performance is improved,which verifies the effectiveness and practicality of the PRM matrix.更多还原