Research On Improved Matching Pursuit Algorithm In Compressed Sensing

With the rapid progress of information technology, the amount of information demand is also growing fast. Therefore, in the process of high speed transmission and storage of large capacity data, the pressure of the hardware system is very large. How to get information effectively is an urgent problem in the field of electronic information. Compressed sensing is a new theory of information sampling and encoding and decoding, which makes full use of the sparsity and compressibility of the signal, and the signal sampling and compression are fused together. For a sparse signal in a high dimensional space, the hope can be effectively reconstructed from a finite number of linear projection measurements, which requires the study of the reconstruction algorithm in compressed sensing. Reconstruction algorithm is one of the key contents in the study of compressed sensing theory. The purpose of the study is to obtain the best reconstruction result with the least cost.This thesis studies the main contents are as follows:(1) Three most critical parts of compressed sensing theory are introduced in this thesis:the sparse representation of signal, the design of observation matrix and the reconstruction algorithm. Several classical greedy reconstruction algorithms are summarized, and the simulation experiments are used to compare the reconstruction rate and time of the algorithm.(2) It may produce a small amount of error reconstruction algorithm to estimate the spectrum, which will have an impact on the accuracy of reconstruction of the time domain signal. In order to improve the accuracy of the reconstruction in the study of generalized orthogonal matching pursuit algorithm (GOMP), the fourier conjugate symmetry applied to atoms of the selection process, a method based on fourier conjugate symmetry of generalized orthogonal matching pursuit algorithm (FGOMP) is proposed. By three aspects of the reconstruction efficiency of the signal, the reconstruction of the relative error and the reconstruction operation time, we can see the feasibility of the generalized orthogonal matching pursuit algorithm based on the fourier conjugate symmetry. The experimental results show that the reconstruction performance of the generalized orthogonal matching pursuit algorithm based on the fourier conjugate symmetry is better than that of the generalized orthogonal matching pursuit algorithm.