Algorithms Of Blind Source Separation In Time And Frequency Domains

Since the original works by Herault, et al, great advances have been made in the area of blind source separation (BSS). It has become a hotspot of modern signal processing. It has many protential applications in communication, speech processing, image processing, biomedicine and radar technology, and it even finds applications in financial data analysis. However, there are still many open issues that need further investigation.In this dissertation, BSS theory is formulated according to the properties of mixing channels and sources. Some new approaches are presented based on the contributions by former researchers.Generally, on one hand, BSS approaches can be classified into two groups according to the mixing channels: approaches for instantaneous mixtures and that for convolutive mixtures. Although instantaneous mixtures are just a special case of convolutive mixtures, it is usually treated differently from that of convolutive mixtures. Under some conditions, BSS approaches of instantaneous mixtures can be generalized to the separation of convolutive mixtures.On the other hand, BSS approaches can be categorized into three classes with respect to statistical information exploited: second-order statistics (SOS), high-order statistics (HOS) and parameters defined in information theory.In addition, BSS approaches can also be time-domain approaches and frequency-domain approaches according to their implementation manner.BSS theory and approaches are studied along these three lines in this dissertation. The main contributions are as follows:(1) BSS theory and approaches for instantaneous mixture separationSOS based BSS theory is formulated with some new considerations. It is proved that the nonstationarity and nonwhiteness of sources play an equal role in BSS. Noise-robust BSS algorithm, which is based on the joint diagonalization of time-delayed correlation matrices, is presented under the assumption of nonstationarity and nonwhiteness properties of sources. It can be implemented in block-based way or online way. Some SOS based approaches by the others are just the special cases of this new algorithm. An adaptive initialization strategy for separation matrix is also presented to overcome the instability of convergence usually suffered by SOS based algorithms. In addition, a fast converging algorithm is presented specially for the separation of two sources.A similar conclusion is also achieved for HOS-based BSS theory. A new algorithm is presented based on the joint diagonalization of symmetric forth-order cumulant matrices.In addition, by applying the SOS based BSS theory to mixtures in frequency domain, a complete frequency domain approach and a half-time half-frequency domain approach are proposed too.(2) BSS theory and approaches for convolutive mixture separationSOS based BSS theory for convolutive mixture separation is formulated and the so-called Double-LMS and Double-RLS algorithms are presented under the simplified convolutive mixing model. The HOS based BSS theory is also investigated under this simplified assumption.BSS is equivalent to the joint diagonalization of power spectral density matrices when the SOS-based BSS theory is applied to convolutive mixtures of nonstationary sources. Integrated objective function with respect to time-domain parameters of separation system is defined according to Hadamard's Inequality in frequency domain. A natural gradient-based algorithm is achieved by the optimization of this objective function. It overcomes the permutation problem and inherits the advantages of high performance and efficient computation from frequency domain approaches.Similar to that mentioned above, the natural gradient algorithm by Amari is also generalized to the separation of convolutive mixtures in frequency domain. An integrated objective function with respect to the time domain parameters of separation system is defined based on Kullback-Leibler divergence in frequency domain. The optimization of this objective function leads to a novel Kullback-Leibler divergence-based BSS algorithm for convolutive mixture separation. It is implemented efficiently with Fast Fourier Transform and does not suffer from the permutation problem.In conclusion, this dissertation brings some new ideas to BSS.