Improved Measurement Matrix Construction with Pseudo-Random Sequence in Compressed Sensing

In compressed sensing theory, the measurement matrix improves the reconstruction performance by reducing the cross-correlation between itself and the sparse dictionary. Aiming at the difficulty of hardware implementation of random measurement matrix and the large storage cost, this paper proposes an optimized method for constructing measurement matrix based on pseudo-random sequence. This method combines the random Gaussian matrix with the pseudo-random sequence and the Hadamard matrix, adjusts the size of the measurement matrix by changing the order of the random Gaussian matrix, so that the constructed matrix not only retains the advantages of the random Gaussian matrix with few measurements and the pseudo-random sequence with high correlation, but also has good reconstruction performance. At the same time, related theorem is proposed and its rationality is verified. Finally, the one-dimensional random signal and two-dimensional images are experimentally verified on the MATLAB simulation platform. The experimental results show that, compared with the conventional matrices, the optimized matrix has better reconstruction performance, lower time computation complexity and good application value.