Research on the Blocked Ordered Vandermonde Matrix Used as Measurement Matrix for Compressed Sensing
Zhao Rui-zhen Wang Ruo-qian Zhang Feng-zhen Cen Yi-gang Hu Shao-hai
(Institute of Information Science, Beijing Jiaotong University, Beijing 100044, China)
(Key Laboratory of Advanced Information Science and Network Technology of Beijing, Beijing 100044, China)
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 non-uniform 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.
赵瑞珍, 王若乾,张凤珍, 岑翼刚, 胡绍海. 分块的有序范德蒙矩阵作为压缩感知测量矩阵的研究[J]. 电子与信息学报, 2015, 37(6): 1317-1322.
Zhao Rui-zhen, Wang Ruo-qian, Zhang Feng-zhen, Cen Yi-gang, Hu Shao-hai. Research on the Blocked Ordered Vandermonde Matrix Used as Measurement Matrix for Compressed Sensing. JEIT, 2015, 37(6): 1317-1322.
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