Research On The Nonlinear Function Of Blind Separation Algorithm Based On Natural Gradient

Blind source separation is a process of recovering the source signals only by observed mixed signals but otherwise unobserved source signals from their mixtures without any prior knowledge of the channel. Increasing attention has been paid on natural gradient algorithm, for one of the core algorithms of blind source separation. Natural gradient algorithm has a good application prospect because of the advantages of low computational complexity, fast convergence speed, good separation effect. Therefore, it has been widely applied in the field of speech signal processing, image processing, wireless communication, and so on.This thesis introduces the background and basic theory of blind source separation. Through the introduction of the three basic models of blind source separation, the solvability of blind source separation is discussed. Several kinds of commonly used cost function are introduced for the point of optimizing algorithms, and lead to the classic blind source separation algorithm, natural gradient algorithm. It also discusses the effect of the nonlinear function. The structure method of nonlinear function and the commonly nonlinear function are given at same time.In order to solve some problems in the case of instantaneous linear mixtures of natural gradient algorithm for blind source separation, especially for the choice of nonlinear function in separation matrix for different source signals, two kinds of improved nonlinear function have proposed. One of that is to improve the problem of considerable error separation caused by using the same nonlinear function for all source signals. Pearson system is introduced and combined with the conventional nonlinear function. Than an improved piecewise nonlinear function has present. It has been proved reducing the error separation of the algorithm without increasing the complexity of algorithm by emulational experiment. The other one is to overcome the shortcoming of missing information caused by nonlinear function, which is selected by the symbol of kurtosis. The new nonlinear function is the combination of Hyperbolic-Cauchy model and kurtosis which represents the source signals information. The simulation results show that the new nonlinear function reduce the mean square error of the algorithm and improve the separation accuracy of the algorithm.