Research On Algorithms Of The Mixing Matrix Estimation In Sparse Component Analysis

Sparse component analysis?SCA?is a new promising approach to solve the blind source separation?BSS?problem in signal processing,which have strong theoretical advantages and wide application prospects.In recent years,SCA method has been widely applied in extensive fields,such as image processing,time-frequency representation,electromagnetic and biomag-netic imaging,filtering,wavelet denoising,neural and speech coding,spectral estimation,fea-ture extraction,fault diagnosis,vector quantization,economy and finance.Particularly,SCA is a very efficient method for the underdetermined BSS problem.The method uses the sparsity assumption of the source signals to estimate the mixing matrix and recover the source signals without any knowledge of them.However,SCA research is just in a developing stage.There are still many problems to be further studied and solved.Especially,the mixing matrix estimation of SCA is a key pre-condition to guarantee the successful recovery of source signals.The problem of the mixing matrix estimation is studied in this dissertation.Firstly,we provide a detailed introduction about the research background and the advances of SCA both at home and abroad.Then some preliminary knowledge about SCA are summarized.Finally,for the two different sparsity as-sumptions of sources,we respectively propose the comparatively efficient and fast algorithms for the mixing matrix estimation.The main works in this dissertation is introduced as follow-ing:1.Under the most sparse assumption of the source signals,we propose a clustering method based on a similarity function to estimate the mixing matrix.The method of SCA in general has two steps:the first step is to identify the mixing matrix A in the linear model X=AS,whereA=(a_ij)_m×n;the second step is to recover the sources S.In the sake of improving the first step,firstly,the kernel parameter of the similarity function is estimated according to the observed signals,so that the proposed algorithm is capable of adapting to different scales of sparse signals.Then,a fixed point algorithm is formulated to optimize the similarity function for estimating the mixing matrix.Finally,the experiments show that in the case of unknowing the number of source signals,our algorithm can choose the appropriate parameters adaptively,and can effectively and accurately estimate the mixing matrix in different small scale problems.The results for the insufficient sparsity sources are also satisfactory;2.Under the weakest sparsity assumption of sources for the identifiability conditions of the mixing matrix?i.e.at the instant time“t”,the number of active sources is m-1,the others are zero?,a novel hyperplane clustering algorithm is proposed to estimate the mixing matrix.We apply an existing clustering function with some modifications to detect the normal vectors of the clustering hyperplanes concentrated by observed data X,then those normal vectors are clustered to identify the mixing matrix A.An adaptive gradient method and an initialization algorithm are developed to maximize the clustering function.The experimental results indicate that the proposed algorithm is faster and more effective than the existing algorithms.Moreover,the proposed algorithm is robust to the two challenging situations:the number of sparse sources points is insufficient,and the sparsity assumption of sources is much sparser.