分块的有序范德蒙矩阵作为压缩感知测量矩阵的研究

Research on the Blocked Ordered Vandermonde Matrix Used as Measurement Matrix for Compressed Sensing

测量矩阵是压缩感知(Compressed Sensing,CS)的重要组成部分,确定性的测量矩阵易于硬件实现,但是重构信号的精度一般不如随机矩阵。针对这一缺点,该文提出并构造了一种新的确定性测量矩阵,称作分块的有序范德蒙矩阵。范德蒙矩阵具有线性不相关的性质,在此基础上加上分块操作和对元素进行有序排列得到的分块的有序范德蒙矩阵,实现了时域中的非均匀采样,特别适合于维数较大的自然图像信号。仿真实验表明,对于图像信号该矩阵具有远高于高斯矩阵的重构精度,可以作为实际中的测量矩阵使用。

The measurement matrix is an important part of Compressed Sensing （CS）. Although the deterministic matrix is easy to implement by the hardware, it performs not so well as a random matrix in the signal reconstruction. To solve this problem, a new deterministic measurement matrix which is called as the blocked ordered Vandermonde matrix is proposed. The blocked ordered Vandermonde matrix is constructed on the basis of the Vandermonde matrix, whose the vectors are linearly independent. Then the block operation is taken and its elements are sorted. The proposed new measurement matrix realizes the nomuniform sampling in the time domain and is specifically suitable for the natural images whose the dimension is usually high. The simulation results show that the proposed matrix is much superior to the Gaussian matrix in the image construction, and can be used in practice.