Underdetermined Blind Source Separation Algorithms And Their Applications In Speech Signal Processing

With the development of information and computer technique,there is a high demand for methods of signal processing.In many applications,only the mixing signals or the mixing signals with noise of the source signals can be obtained by the sensors,how to separate the original source signals from the mixing signals is the problem that must to be solved in some applications,the technique of blind source separation(BSS) is being developed under this circumstance.Many researchers have devoted themselves to this area when the technique was put forward.As a new method of data processing,BSS is the result of the combination of the artifical neural network,statistical signal processing,information theory and computer science.And will be of great value in a lot of applications such as biomedicine,medical image,speech signal processing,communication system, information retrieval and so on.The technique of BSS is to recover or estimate the original signals from several observed mixed signals according to less prior information without any knowledge of the sources and channels.The prior information is the basic hypothesis of the blind source separation,i.e.the sources in the mixing signals are independent each other.This condition is not strict so the technique of BSS has wide applicaions in many areas,and recently,it has been one of the most active research areas in the modern signal processnig.In the earlier research of the BSS,generally,to simplify the research work, BSS methods mostly concentrate on the overcomplete case or complete case,that is,the number of observed signals is not less than that of source signals.However, with the development of the blind signal processing,as the extension of the standard BSS,underdetermined BSS has attracted a great deal of attention recently, in this case,the number of observed signals is less than that of source signals, because the system is not linearly invertible,so the research method is different from that of the standard BSS,recently the main method of the underdetermined BSS is based on the overcomplete representation and the sparse representation.This dissertation reviews the development of BSS,the current research status, the related theory and classic algorithms systematically,lots of exploratory research work has been done around the key techniques of underdetermined BSS, which include the separability,the estimation of the number of sources,the handling of the signal sparseness and nonlinear separation method and so on,some separation algorithms has been proposed,these contents are belong to extended BSS,and has considerable theoretical value and practical value.Also,as the application of BSS,we have done some research work on speaker recognition。Overcomplete representation is an extended BSS algorithm,it has a great flexibility in capturing the structures of the signal,not only can solve the underdetermined BSS,but also can obtain the basis functions which describe the high order statistical information of the signal.Base on these basis functions,a text Independent speaker recognition system was built,experiments result shows that this kind of features can gives better recognition rate.The main contributions of this dissertation are consists of the following parts:1.In the algorithm of overcomplete representation,the algorithm can be divided into two steps,frist estimating the sources when the mixing matrix is fixed, then training the mixing matrix when the sources are fixed.In the case of two or not too many observed mixing signals,the shortest path decomposition is proposed to estimate the source signals in the frist step,which can enhance the training speed and can avoid the computation of the invertable matrix.2.In the two steps algorithm of underdetermined BSS,the accurate mixing matrix estimation is the precondition for separation,after sparse processing,a new weighted potential function has been used,in the lower resolution we can estimate the number of sources accurately,also in the neighborhood of the clustering directions,higher resolution is used to estimate the mixing matrix.Experiments results show that this method can give better estimation even if the observed signals are contaminated by noise.3.In the separation method of underdetermined case,the traditional method of minimization of L~1 norm can give the certain solutions,this algorithm was obtained at the maximum aposteriori probability(MAP) of source signals,and can not achieves the theoretical optimal value when using the linear programming method, especially when the sourse signal is not sparse enough.Two methods are proposed to overcome the disadvantage of the L~1 norm method.First,a weighted algorithm at the clustering directions is proposed,this method can described the sources better and can gives higher SNR than that of L~1 norm method,especially can avoid the separation failure when small amplitude source in observed signals.Second a least mean square error algorithm is proposed,this method can trace the inner variety of the sources when searching the optimal separation sub-matrix,also can gives higher SNR than that of L~1 norm method,by comparison with sources,the separating performance is satisfied and have the practical value.4.Algorithm of noisy underdetermined BSS.Noise can influence the algorithm performance,however,algorithm of BSS with denoising is difficult to implement,for this reason,time-frequency transform are usually used to denoise the observed signal before separation.An algorithm based on higher order statistical sparse feature is proposed,which utilizes the "concentration" feature of wavelet transform to denoise.After the wavelet transform,the information of signal is concentrate on less wavelet coefficients,this not only achieved sparse processing,but also achieved denoising in wavelet domain.Also this method is suitable for BSS model and BSS prior hypothesis,and has an advantage than that of method which based on second order statistical sparse feature,experiment result show better separation performance.5.The application in speaker recognition.Effective features are always the key problem in recognition systems,also in the speaker recognition system.For speech signal,not only include the physical informations of speaker,but also include the semantic information of speech,research results have shown that these two kinds of informations can be considered to be independent each other,this feature is very suitable to BSS model.We use the technique of the overcomplete representation to divided signal into linear combination of basis functions according to setting the distribution of the coefficients of the basis functions,if the coefficients are sparse or have the super-gaussian distribution,the obtained basis functions can describe the higher order statistical structure of the signal.These basis functions can be used in the speaker recognition system or speech recognition system,after training large numbers of speech signal,we can get the basis functions which is correlative to the speaker information,experiment result shown the feature is effective.In sum,around the probability statistical method,sparse handling,nonlinear separation and time frequency transform techniques,underdetermined BSS method are investigated in this dissertation,combined with the application,BSS technique has successfully used in speech signal processing.Finally,the problems to be solved related to this research area and future research topics are summarized,furthermore, the prospect of the developing tendency is analyzed as well.