元素随机排列的傅里叶测量矩阵构造方法

摘要

针对压缩感知理论在超宽带信号低速采样的应用过程中，现有测量矩阵随机变元多、重构效果有待进一步提高的问题，结合傅里叶矩阵和托普利兹矩阵的构造特点，提出元素随机排列的傅里叶测量矩阵构造方法。该方法先以各元素服从正态分布的方式随机生成一行向量并对其进行傅里叶变换，再通过随机排列变换后向量元素的方法生成矩阵各行从而得到随机傅里叶测量矩阵。仿真实验表明，使用该测量矩阵在同等条件下相比于高斯、伯努利等随机矩阵，信号具有更好的重构效果。同时，该测量矩阵比高斯随机矩阵拥有更少的随机变元数目。%In this paper,with the combination of the structural features of the Fourier matrices and Toeplitz ma-trix,we proposed the Fourier measurement matrix with random permutation to reduce the number of random variables as long as improved the reconstruction performance for low rate UWB signal sampling with compressed sensing.We first randomly generated a row vector whose entries comply with the norm distribution,then we randomly permuted the entries of a new vector,which was the output of the fast Fourier transform of the vector we mentioned before,to achieve different row vectors to form the measurement matrix.Simulation results showed that under the same condition,the signal had a better reconstruction performance using the proposed measurement matrix rather than Gaussian/Bernoulli random matrix.Besides,compared with Gaussian random measurement matrix,the proposed method effectively reduced the number of random variables.