Design Of Measurement Matrices Based On Compressed Sensing And The Applications Of The Matrices In Image System

Compressed sensing theory is a new theory with the continuous development ofthe information society. As people call for more stringent requirements for the storageand transmission of the information, the traditional signal compression method isdifficult in some ways to meet people’s requirements. So compressed sensing theorycame into being. This new theory is not based on the traditional Nyquist theorem, butto break this limit, making the sampling process of the signal not have to satisfy theNyquist theorem, thus greatly reducing the sampling rate. Due to the reasons above,compressed sensing has gained more and more attention in recent years. Thecompressed sensing system consists of two parts, one is signal sensing and the other issignal reconstruction. For the sensing part, the quality of the measurement matriceshas a significant impact on the accuracy of signal reconstruction.In this paper, we conducted a study of three core issues of compressed sensing,including the sparse signal representation, design of the measurement matrices, andthe recovery algorithm. Then, the existing constructing methods of measurementmatrices have been introduced in this paper. In order to solve the problem that for theLDPC matrices, complex experiment must be done to determine the optimal value ofd(the number of “1” in each column) when the dimensions of the measurementmatrices are different, we suggested a low-complexity method which can generatesemi-cyclic semi-random measurement matrices. The proposed measurement matricescan be generated without calculating the optimal d, and they also have a binarystructure which can be easily implemented in hardware. Compared with the LDPCmatrices, the new matrices are more sparse. These matrices can also be used in thecompressed sensing image system, and have good reconstruction results.For image reconstruction of compressed sensing, simulation experiments verifiedthat the proposed semi-cyclic semi-random matrices outperform other existing CSmeasurement matrices. When used in compressed sensing image system, the matricesnot only can be easily implemented in hardware, but also have excellent recoveryresults.