Research On Compressive Sensing Sparse Reconstruction Algorithm For Undetermined Blind Source Separation

Compressed sensing(CS)is a new signal processing technology,which breaks through the limitation of the traditional Nyquist theorem on the sampling rate.And the data acquisition and data compression are accomplished at the same time,realizing the rapid and efficient data processing.CS has been applied to many fields,Underdetermined blind source separation(UBSS)is one of its application field.Due to the CS and UBSS have the similar mathematical model,and when the mixed matrix estimation in UBSS is completed,The difficulty faced by both theory is to reconstruct the source signal.At present,the research of sparse reconstruction algorithm of compressed sensing source signal is relatively mature.Therefore,the compressed sensing sparse reconstruction algorithm is used to the UBSS,which is possible to satisfactorily complete the source signal recovery in the UBSS.In this paper,we mainly study the compressed sensing sparse reconstruction algorithm for UBSS.The work of this thesis can be summarized as following aspects:(1)The existing sparse reconstruction algorithm can reconstruct source signal only when the sparse degree of the source signal is less than or equal to half of the length of the observed signal.Aiming at this shortcoming,the sparse reconstruction algorithm based on the partial support set is proposed.This algorithm changes the original mathematical optimization model based on L1 norm reconstruction algorithm,minimizing the partial value of the component in the source signal as the objective function.The constraint condition is still the mathematical equation which satisfies the compressed sensing,Linear programming method is used to solve the new mathematical optimization model,achieving the source signal exactly reconstruct.The proposed algorithm breaks the bottleneck of the existing algorithm to the degree of sparseness.It can still realize the reconstruction when the sparse degree of the source signal is more than half of the length of the observed signal,and under different SNR and sparse degree conditions,The proposed algorithm has better reconstruction precision than that of OMP,BP and LASSO.(2)For the shortest path method only applies to the case where the observation signal number is two,the idea of traversal for average is used to it,the improved algorithm is suitable for the multi-channel observation signal source signal recovery.Secondly,an improved statistical sparse decomposition(ISSDP)algorithm is proposed to solve the problem faced by the statistical sparse decompositio(SSDP)algorithm,only when the number of active source signal is equal to the number of observed signals to rescover the source signal.The ISSDP algorithm is not only suitable for insufficient sparse but also for fully sparse conditions with lower time complexity,higher correlation coefficient and the signal to interference ratio.In addition,the CMP,L1 CMP,SCMP algorithms based on CS are applied to UBSS,verifying the superiority of the algorithms in the case of fully sparse.(3)The UBSS technology is applied to the radar signal processing.Using different algorithms to recover the full sparse and non-full sparse radar source signal in time domain,and scatter it non-sufficiently in the time domain but recover it in the wavelet domain respectively.Result show that if the source signal is not sufficiently sparse in the time domain,it can be transformed to the wavelet domain,then use the algorithm of CS to complete the signal recovery.