The Research Of Blind Source Separation Algorithms Based On Clustering And Undecimated Wavelet Transform

Blind Source Separation,an active research field in modern signal processing fields,refers to recovering source signals from the observations received by sensors with the source signals and transmit channel unknown.Blind source separation technology is widely used in reality.It has made great achievements in application,especially in speech and image processing,communication system,machinery test,biomedicine and so on.According to the relationship between the number of the observations and source signals,blind source separation can be classified into three categories,that is,overdetermined blind source separation,determined blind source separation and underdetermined blind source separation.If there is noise in the mixing process,noisy blind source separation appears.The “two steps” method is usually utilized for underdetermined blind source separation where the number of source signals is larger than observations' and Independent Component Analysis(ICA)is widely used for determined blind source separation where the number of source signals is equal to observations'.While it is effective to using the combination of one denoising method and ICA to deal with noisy determined blind source separation.In this paper,we focus on studying the two models: underdetermined blind source separation and noisy blind source separation.Algorithms to the two models are proposed based on digesting theories related to the “two steps”,such as sparse representation of signals,clustering analysis of estimating mixing matrix and linear programming method about recovering source signals,criterions of independence and optimization algorithms about ICA and threshold denoising methods.The main work and contributions are summarized as follows.1?A new method to estimate the underdetermined mixing matrix is proposed.Among the methods of clustering analysis,K-means algorithm is a conventional and simple method.It is easy to operate and well suited to compact or globular clusters.However,K-means needs the number of source signals in advance.Besides,it is extremely sensitive to initial conditions.Different initial conditions give extremely unstable results of clustering.While AP(Affinity Propagation)which uses the principle of affinity propagation doesn't need to know the number of source signals in advance.It can exactly provide the number of source signals and initial centers.AP clustering combined with K-means is utilized to estimate mixing matrix in this paper.The number of source signals and initial centers are searched out by AP in the first step,based on which K-means algorithm is utilized to obtain accurate mixing matrix.Experimental results prove that the K-means algorithm initialized by AP clustering can estimate a more stable and accurate mixing matrix than conventional K-means can.2?A method based on Undecimated Wavelet Transform(UWT)and FastICA is proposed to accomplish noisy blind multiple images separation.Undecimated Wavelet Transform can preserve more complete information of image,which outperforms orthogonal wavelet transform at image denoising.In this paper,we propose the Undecimated Wavelet Transform to denoise the noisy mixed images for the first time and then utilize FastICA to separate images.The simulation results show that the proposed method can realize noisy blind multiple images separation by the way of denoising followed by separating.