Studies On Signal Reconstruction Algorithms Of Compressive Sensing

Compressive sensing is a new type of digital signal processing method. The novel objective of compressive sengsing is to reconstruct a signal accurately and efficiently from far fewer sampling points got by Nyquist Sampling Theorem.Compressive sensing theory combines the process of sampling and compression to reduce the complexity of signal processing, which is widely used in many fields. Signal reconstruction is an essential part of the compressed sensing. This paper focuses on the algorithms of signal reconstruction.Firstly, the basic principle of compressive sensing, including the costruction of sparse signals, the measurement matrix and the basic idea of recongstruction algorithms is analyzed. Based on the theory of compressive sensing, the main reconstruction algotithms are summed up. Special charaters and the existence of expander graphs are discussed.Secondly, minimum l1 -norm reconstruction algorithm and Orthogonal Matching Pursuit (OMP) reconstruction algorithm are deeply studied in this paper. The realizable schemes of two methods are ananlyzed, and the solving process of minimum l1 -norm algorithm is researched. Then the simulation flow charts of two algorithms are given. We analyze the performance of minimum l1 -norm algorithm and OMP algorithm by the simulation results, respectively study the relationship amony reconstruction accuracy of the algorith,sparsity level of signals and the number of measurement entries with different input signals.Finally, the signal reconstruction algorithm using expander graph is studied. We designed the simulation system and flow of reconstruction algorithms using expander graph for sparse signal and approximate sparse signal. Explicit constructions of the considered expander graphs are very difficult. According to the theorems, we randomly generate a regular bipartite graph with a uniform distribution as the expander graph for simulation. We ananlyze the feasibility and characters of the recovery algorithm using expander graph under different input singals. Finally, we compare the accuracy of reconstruction and the recovery time of three algorithms, and analyze the respective advantages of algorithms.