Research On Methods Of Multi-set Joint Blind Source Separation

Joint blind source separation (J-BSS) is an emerging topic with particular interests in multi-set signal processings. Compared with the conventional single-set BSS, J-BSS can utilize more relevant information of the multi-set signals. Therefore, it is able to generate improved performance than BSS and has broad application prospect.Recently, generalized joint diagonalization (GJD) has been proposed to address the J-BSS problem. More exactly, these methods first construct target matrices with particular GJD structures by using the inherent multi-set statistic (e.g. inter-set dependence and intra-set independence)., and then identify the mixing mechanism as well as the latent variables of all the datasets jointly by fitting the GJD structure of these matrices in an algebraic manner. However, there is still a lack of comprehensive study for GJD in the literature, and several limitations exist for GJD with regards to the orthogonal limits, robustness to noise, and convergence properties, etc.This thesis provides a thorough study on the methods of multi-set J-BSS with GJD. Several orthogonal and non-orthogonal GJD algorithms with advanced performance are developed and their applications to real-world J-BSS problems are studied. The main contributions are:● A simple non-orthogonal JD algorithm for J-BSS of two datasets is proposed based on LU decomposition and successive rotations. The experiment has demonstrated its superiority over other similar algorithms with regards to convergence and accuracy.● A generalized non-orthogonal JD (GNJD) algorithm for J-BSS of more than two datasets is proposed based on LU decomposition and successive rotations. Experiments have demonstrated its nice performance with regards to convergence, robustness to noise, and permutation alignment. In addition, two parallelization methods for GNJD are developed for further acceleration, especially when dealing with large matrices. Experiments show that these strategies can largely reduce the running time without sacrificing the accuracy.● A Givens rotation based generalized orthogonal JD (GGOJD) algorithm is proposed by converting the multi-parameter optimization problem into a series of simple eigenvalue decomposition problems through matrix factorization. The experiments have illustrated its advantage over existing similar algorithms in both convergence and accuracy.● Two real-world GJD applications are examined:e.g. fetal electrocardiography (ECG) separation and frequency domain speech separation. The proposed GNJD and GGOJD algorithms are challenged by several JD and GJD methods in these applications. Experiments results have shown that the proposed algorithms extract more fetal ECG information and improve the separation accuracy of speech.