Research On Block Sparse Signal Reconstruction Algorithms

Compressive sensing theory is an emerging processing technology in the field of signal processing in recent years.This novel processing framework,which combines signal acquisition and compression,has been widely used for reducing the redundancy and waste of data.Compressive sensing requires that the signals are sparse or after some sparse transform.Most of the actual signals satisfy this condition and have a specific intrinsic structure.Block sparse signals with nonzero coefficients appeared in clusters are very common in practice and have become the hotspot of the compressive sensing theory.Firstly,from the basic principle of the compressive sensing,the common greedy algorithms and the Sparse Bayesian Leaning algorithm(SBL)are introduced in detail.The simulation experiments of these algorithms are compared,and their reconstruction performances are analyzed.Secondly,in view of the characteristics of fast calculation speed of greedy algorithm,the block greedy algorithms are studied.Based on the detailed analysis of the existing block greedy algorithms,two improved algorithms are proposed,i.e.,the BOMP algorithm based on the correlation coefficient(CBOMP)and the block BAOMP algorithm(BBAOMP).In the case of known signal blocks,CBOMP algorithm uses the strategy of the correlation coefficient between the vectors to select atomic block and can estimate block length adaptively.BBAOMP does not need the information of the block structure.It uses the piecewise continuous property of block sparse signal to avoid the missing of the correct atoms by incorporating adjacent atoms of the selected atom into the support set and uses the backtracking mechanism to delete the selected wrong atoms.Simulation experiments show that the proposed algorithm can recover block sparse signals more effectively than existing algorithms.Thirdly,since Bayesian reconstruction algorithm has good noise resistance and practical application,this paper studies the Pattern Coupled Sparse Bayesian Learning algorithm(PCSBL)and the adaptive pattern coupled sparse Bayesian learning algorithm.On this basis,a simplified adaptive pattern coupling sparse Bayesian learning algorithm(SPCSBL-DDCP)is studied in this paper,and a set of adaptive coupling parameters is used to reduce the computational complexity of the algorithm.Furthermore,considering the correlation between the adjacent elements in the block sparse signal,a weighted block sparse Bayesian learning algorithm(WBSBL)based on the weighted mean idea is proposed by introducing a parameter to compute the weighted average of the adjacent elements of the signal.Compared with the existing algorithms,the reconstruction speed is improved and the reconstruction accuracy is maintained.Finally,a weighted mean block sparse Laplace Bayesian reconstruction algorithm(WBSBL-Laplace)is proposed,and the reconstruction of the block sparse signal for the Laplace layered model is realized.This paper also further studied the multiple measurement vector(MMV)model.For the multiple measurement model in the case of block sparse signals,the aforementioned block sparse reconstruction algorithms are further extended to multiple measurement vector models,i.e.,a block orthogonal match pursuit multiple measurement vector algorithm(SCBOMP)based on correlation coefficient,block backtracking matching multiple measurement vector algorithm(SBBAOMP),weighted average Bayesian block sparse reconstruction algorithm based on multiple measurement vectors(MDWBSBL)are proposed,and simulations verify the performance of these algorithms.