Study and Construction for the Compressed Sensing Measurement Matrix Which is Easy to Hardware Implementation

Abstract

In the compressed sensing process, measurement matrix plays a significant role in signal sampling and signal reconstruction. Therefore, to construct measurement matrix which is simply-structured, has small memory and is easy to be implemented into hardware is the key to put the compressed sensing theory into application. On the basis of study on Partial Hadamard measurement matrix and Pseudo-Random Sequence, this paper brings up two measurement matrixes which are easy to put into hardware, namely sequence partial Hadamard measurement matrix and circulant pseudo-random sequence measurement matrix, in which the latter consists of the circulantm sequence and circulant gold sequence measurement matrix. It further proves that measurement matrix constructed by pseudo-random sequence complies with the RIP principle. To test the performance of the two measurement matrixes, the paper tries to simulate the two-dimensional image signal. It is found that, under low sampling, the reconstruction of the sequence Partial Hadamard measurement matrix is optimal with the premise that the length of the sampling signal must be $2^{\text{k}}$. Though it is inferior to the sequence Partial Hadamard measurement matrix, the reconstruction of the circulant pseudo-random sequence measurement matrix excels Gaussian random measurement matrix, and also overcomes the sequence Partial Hadamard measurement matrix’s $2^{\text{k}}$-length limitation. In a word, the two kinds of measurement matrix are easy to be implied into hardware, can avoid the uncertainty of the random matrix and also overcome the wasting storage of random matrix. Therefore, they have good practical application values.