Research On Several Problems In Blind Source Separation Based On Generalized Eigendecomposition

Blind source separation (BSS) is to separate the source signals from the mixing signals without prior knowledge of the source signals and the transmission condition. It has been a focus in the research area of signal processing and neural networks. And it has been widely used in wireless communication, sonar and radar systems, medical signals processing, image processing, and so on. In this dissertation, the algorithm of the blind source separation based on generalized eigendecomposition is mainly investigated. The primary contributions and original ideas included in this dissertation are summarized as below.(1)For the problem of the blind source separation of noised signals, wavelet de-noising algorithms are applied in the pretreatment process of BSS. Based on summarizing and analyzing the advantages and shortcomings of various methods, a multi-scale de-noising algorithm based on the convolution type wavelet packet transform is presented to be applied in the pretreatment process of BSS. The algorithm ensures the precision of the noisy BSS model.(2)Blind source separation based on generalized eigendecomposition using dyadic wavelet is proposed. By the method of dyadic wavelet transform, the mixing signals may be highly non-gaussian. In the meantime, the transacted signals are separated by the method of generalized eigendecomposition. Effectivity and performance of the new algorithm are demonstrated by the computer simulations.(3)In view of the limitations of the current generalized eigendecomposition blind source separation methods for the non-stationary signals, a new method for blind source separation based on the generalized eigendecomposition using empirical mode decomposition (EMD) is presented. In comparison to wavelet transform, EMD has more predominance about time-frequency resolution and will not cause spectrum-leakage influences, so better separation results to non-stationary signals are obtained by the new algorithm. Avoiding the wavelet base selection, the algorithm is more simple and easy to implement due to the adaptivity of EMD.(4)According to nonlinear BSS problem, linear BSS algorithm based on generalized eigendecomposition is extended to nonlinear cases. By the use of kernel function, the mixing signals are mapped to high-dimensional feature space, and the nonlinear mixing model in sample space is transformed to a linear mixing model in nonlinear feature space. Then BSS based on generalized eigendecomposition using dyadic wavelet is employed to separate the mapped signals. The new algorithm dose not hypothesizes too much about the probability density of source signals, and optimal iterative isn't applied in the procedure. So the algorithm is easy to implement.