Study On Blind Source Separation With Unknown And Dynamically Changing Source Number

Blind source separation (BSS) consists of recovering mutually independent butotherwise unobserved source signals from their mixtures without any prior knowledge ofthe channel. BSS has attracted growing attention in statistical signal processing andunsupervised neural learning society, since it is a fundamental problem encountered invarious fields, such as wireless telecommunication systems, sonar and radar systems, audioand acoustics, image enhancement, biomedical signal processing, and so on. In thisdissertation, we investigate the problem of over determined blind source separation with anunknown and/or dynamically changing source number, with great emphasis on theexistence of its contrast function and its adaptive parallel implementation. The primarycontributions and original ideas included in this dissertation are summarized blow:1. The BSS problem is systematically addressed. Based on the signal model, we analyzethe indeterminacy inherent in BSS and the basic assumptions of the BSS problem. Thecontrast function theory and the local stability theory are investigated. After that, wealso discuss various forms of existing BSS algorithms and the corresponding localstability conditions. Finally, we present two performance indexes used to measure theseparation performance of the BSS algorithms.2. The over determined BSS with an unknown source number is considered. A newde-mixing model which is applicable to the BSS with an unknown source number isproposed, the separated state under the new de-mixing model is defined. Theseparableness of the new de-mixing model is studied: it is proved the new de-mixingmodel have C_m^m-n essentially non-equal separating points. The existence of thecontrast function is also studied: it is proved the mutual information of the newde-mixing model's outputs is still the contrast function of the over determined BSSwith an unknown source number, each local minimum corresponds to a separatingpoint. The natural gradient algorithm for BSS with an unknown source number isdeveloped by minimizing the contrast: mutual information with natural gradient.3. A kind of semi-parameter statistical algorithm for BSS with an unknown number ofsources is proposed. Firstly, we analyze the behavior of the natural gradient algorithm.It is found that the natural gradient algorithm has no stationary point and there existredundant movement along the null space of the mixing matrix's transpose. Theredundant movement make the norm of the de-mixing matrix diverges to infinite, andthus make the algorithm diverge. To develop a algorithm which can perform the BSSwith an unknown source number and converge stably, the semi-parameter statisticalapproach is introduced into this case: the estimating function in this case isconstructed, the adaptive algorithm based on the estimating function is deduced. Thenew algorithm take any a separating point as it's stationary point. We also analyze thelocal stability of the new algorithm. The sufficient condition to the local stability isobtained.4. The projected natural gradient and corresponding algorithm is deduced. Be aware of itis the redundant movement that cased the natural gradient BSS algorithm with anunknown source number divergent. Based on the orthogonal decomposition of thevector space, we get the projected natural gradient by canceling the component amongthe natural gradient, which is parallel to the null space of the mixing matrix'stranspose, with orthogonal projection. It is proved the projected natural gradient BSSalgorithm with an unknown source number will converges to a limit cycle whichcontains only two point, one is the separating point. The projected natural gradientalgorithm is free of redundant movement;it can perform the BSS with thedynamically changing source number and need not to initialize the algorithm as thesource number changes. What's more, the separated signals are reserved in theoriginal channel. Finally, the ideal of canceling the redundant movement byorthogonal projection is generalized to a kind of RLS BSS algorithm and deduced aRLS BSS algorithm with an unknown source number.