Study On The Compressed Sensing Reconstruction Algorithms

Compressed sensing is a rising novel sampling theory in recent years, which is different fromNyquist sampling theory. In this theory, signal sampling is able to break the sampling frequencylimit of Nyquist sampling theorem and the sampling rate is no longer subject to signal frequencyspectrum, but related to the signal information structure. Under the premise condition that the signalis sparse or compressible, the data compression can be executed during signal sampling but notprocess these at two steps separately so that the collection of a large amount of useless data can beavoided and the cost of sampling time and resources is reduced.A reconstruction algorithm is one of the core techniques of compressed sensing theory, whichdirectly determines whether the compressed sensing can be applied to actual system or not.Research on reconstruction algorithms mainly includes two aspects, the reconstruction precisionand algorithm complexity. The reconstruction accuracy shows the algorithm performance andeffectiveness, and the algorithm complexity is a key factor that constrains the wide application ofcompressed sensing. This paper mainly studies the matching pursuit(MP)-family algorithms, whichhave simple structure, easy realization and low complexity. The improvement and innovativeresearch on MP-family algorithms is made respectively from these two aspects.The maximum correlation matching of orthogonal matching pursuit algorithm is a globaloptimization process which takes a long time. The particle swarm algorithm can be used to find theoptimal solution for time saving, but the particle swarm algorithm is easy to fall into local optimum,which reduces the algorithm accuracy seriously. Aiming at this problem, quantum particle swarmalgorithm is used to optimize the OMP algorithm for a more accurate signal reconstruction, whichhas better global optimization ability. At the same time, least squares secondary matchingprocessing is proposed after optimization, to further improve the reconstruction precision.Simulation results show that the orthogonal matching pursuit algorithm with secondary matchingbased on the quantum particle swarm algorithm has higher accurate reconstruction probability andlower complexity than that based on the particle swarm algorithm.Sparsity adaptive matching pursuit algorithm is an excellent one from MP-family algorithms,and it can achieves high precision reconstruction while the sparsity of signal is unknown. However,redundant update calculations are included in the algorithm. To solve the problem, a fast sparsityadaptive matching pursuit algorithm is presented, which eliminates the redundant calculations in thebackward pursuit process of sparsity adaptive matching pursuit algorithm. The support set expandsfaster in the proposed algorithm and the reconstruction efficiency is greatly improved. Simulation results show that the fast sparsity adaptive matching pursuit algorithm has the much fasterreconstruction speed compared with the sparsity adaptive matching pursuit algorithm while thereconstruction precision of the fast sparsity adaptive matching pursuit algorithm is similar to that ofthe sparsity adaptive matching pursuit algorithm.MP-family algorithms have excellent performance and simple structure, but the reconstructionperformance of these algorithms is poor in the reconstruction of signals which are an expressionbased on a redundant dictionary due to that the atoms of a redundant dictionary are highly relevant.Based on the oblique projection theory, oblique projection based matching pursuit familyalgorithms are proposed, in which the traditional maximum correlation matching is replaced by theoblique projection matching, to improve the signal reconstruction precision based on the redundantdictionary. Simulation results for multi-source linear frequency modulated signal reconstructionshow that the reconstruction performance of the proposed algorithms is far superior to that of theMP-family algorithms.Using compressed sensing the frequency parameter estimation of linear frequency modulatedsignal can greatly reduce the signal sampling rate. The proposed sparsity adaptive obliqueprojection matching pursuit algorithm is used to estimate the frequency parameter estimation oflinear frequency modulated signal. The estimation performance is further improved. Simulationresults show that the estimation performance of the sparsity adaptive oblique projection matchingpursuit algorithm is far superior to that of the sparsity adaptive matching pursuit algorithm.