Research On Efficient Reconstruction Algorithm In Compressed Sensing

Compressed Sensing(CS)theory shows that,for sparse signals,the number of samples used to accurately recover the original signal can be less than that specified by Nyquist theorem.And the signal sampling and data compression are realized simultaneously without depending on the signal bandwidth.The main work of this paper is to deeply study the efficient reconstruction algorithm in compressed sensing.The chapters include:(1)The principle frame of compressed sensing is introduced.Firstly,several sparse bases and expression dictionaries in sparse representation theory are analyzed and compared briefly.Secondly,the measurement matrix is analyzed,including the conditions that measurement matrix must satisfy and the classification of the measurement matrix.Finally,the signal reconstruction model and several reconstruction algorithms are given.(2)Backtracking matching pursuit algorithm based on inner product accumulation proportion(IPAP-BMP)and backtracking matching pursuit algorithm with double threshold atom selection(DTBMP)are proposed.Firstly,the common reconstruction algorithms are studied.Aiming at the problem that the number of atoms selected in the subspace pursuit(SP)algorithm is fixed and relatively more,the probability that the error atom is selected is increased,reconstruction performance is poor,the atom selection mode is improved and the IPAP-BMP algorithm is proposed.The method of inner product accumulation proportion is used to select atoms in this algorithm.The number of atoms selected is adjusted adaptively according to the distribution of inner product,and then the backtracking mechanism is utilized to eliminate the wrong atoms.Theory and simulation results show that the reconstruction success rate of the proposed algorithm is significantly higher than that of the SP algorithm and other traditional algorithms.The reconstruction error is reduced by more than 60%,and the reconstruction time is reduced by more than 30%.In order to further optimize the performance of the IPAP-BMP algorithm,the inner product module length proportion method is proposed to divide the selection of atoms into pre-selection and check to improve the signal reconstruction accuracy,and an improved DTBMP algorithm is proposed.The simulation results show that compared with IPAP-BMP,DTBMP can reduce the average reconstruction error by 13.8%.(3)A sparsity adaptive matching pursuit algorithm with variable proportion(VP-SAMP)is proposed.The sparsity adaptive matching pursuit(SAMP)algorithm can reconstruct the original signal without knowing the sparsity in advance.However,the number of atoms pre-selected increases with the number of stages,and there is a problem that the number of atoms pre-selected exceeds the measurement value in the case of large sparse degree,which makes it impossible to reconstruct.In order to improve the reconstruction performance of SAMP under large sparsity and optimize its atomic pre-selection method,a VP-SAMP algorithm is proposed.The algorithm first uses the inner product accumulation proportion method to pre-select atoms.Furthermore,aiming at the problem that a single fixed ratio cannot simultaneously meet fast reconstruction of small sparsity and high reconstruction success rate of large sparsity,the algorithm adjust the pre-selected inner product accumulation proportion threshold within the setting upper limit as the number of phases increases,such that the number of atoms pre-selected at a large sparsity does not exceed the number of measurement values,at the same time a sufficient number of atoms can be provided to improve the reconstruction performance.The simulation results show that the reconstruction success rate of the proposed algorithm at large sparsity is 5.8% averagely higher than that of SAMP under the condition that the reconstruction error and the reconstructed time are the same as that of SAMP.And when the sparsity is more than half of the measurement value,it maintains a relatively high reconstruction success rate.