Study On Algorithm For Blind Source Separation

Blind source separation (BSS) consists of recovering mutually independent but otherwise unobserved source signals from their mixtures without any prior knowledge of the channel. BSS has attracted growing attention in statistical signal processing and unsupervised neural learning society, since it is a fundamental problem encountered in various fields, such as wireless telecommunication systems, sonar and radar systems, audio and acoustics, image enhancement, biomedical signal processing, and so on. In this dissertation, we study the blind source separation problem. The primary contributions and original ideas included in this dissertation are summarized blow:1. The BSS problem is systematically addressed. Based on the signal model, we analyze the basic assumptions of the BSS problem and the indeterminacy inherent in BSS. The contrast function theory is investigated. After that, we also discuss various forms of existing BSS algorithms. Finally, we present two performance indexes used to measure the separation performance of the BSS algorithms.2. According to the cumulant based approximation to the mutual information contrast function, the EASI (Equivariant adaptive Separation via Independence) learning rule is optimized by multiplying the symmetric part with an optimal time variant weight coefficient. The cumulant based approximation to the mutual information contrast function is decomposed into a whitening contrast function and a BSS contrast function under whitening constraint and their relative gradients are calculated. The optimal ratio of symmetric part to skew-symmetric part in EASI algorithm is obtained, an optimized EASI algorithm is proposed by multiplying the symmetric part with the optimal time variant weight coefficient, and the stability of the proposed algorithm is given. Simulation results show the proposed optimized EASI algorithm outperforms the existing algorithm in convergent speed and steady-state accuracy.3. The problem of blind source separation is addressed. The natural gradient algorithm with an unknown number of sources exist redundant movement and efficient movement. The projected natural gradient algorithm is free of the redundant movement. It can realize blind signal separation with an unknown number of sources and converge steadily. The projected natural gradient algorithm and the natural gradient algorithm have identical convergent speed. Inspired by this, using the computer simulation, we proved, as the RLS algorithm for well-determined blind source separation is generalized to over-determined blind source separation, there exist similar redundant movement. By canceling the redundant movement of the RLS algorithm for over-determined blind source separation in the orthogonal project approach, the new RLS algorithm for over-determined blind source separation can converge steadily.