Rational Function ICA Algorithm For Blind Source Separation

Blind source separation(BSS)is the process of separating the source signals from the mixed-signal with unknown sources and mixed modes.Independent component analysis(ICA)method is one of the effective methods for blind source separation.It is a mathematical tool for extracting factors or components from multivariate data on the premise that the signals are mutually independent and non-Gaussian.Independent component analysis is developed by blind source separation problems,which has become a powerful tool for signal processing and data analysis.Since the precondition of the source signals is mutually independent which is easy and realistic,ICA has been widely used in the fields of speech signals processing,biomedical signals processing,finance,etc.This thesis addresses three famous algorithms including Infomax algorithm,the Extended Infomax algorithm and Fast ICA algorithm(Fixed-Point algorithm).Infomax algorithm is based on information maximization principle,however,it is only effective in separating sources with super-Gaussian distributions.Because of the matrix inversion in the iterative formula,its cost is expensive.The Extended Infomax algorithm can separate the elements from the mixture of super-gaussian and sub-gaussian signals effectively.However,Switch function of the Extended Infomax algorithm needs to choose various nonlinear functions which makes it ineffective.Fast ICA algorithm has fast convergence rate,but the accuracy of the separation is not as good as the Extended Infomax algorithm.In this paper,we propose the rational function ICA algorithm,which is achieved by applying a rational function directly to a nonlinear function.The rational function ICA algorithm avoids the selection process of switching functions.Numerical results demonstrate that the rational function ICA algorithm is more effective with a high validity.The paper is organized as follows:Chapter 1,we introduce the development of blind source separation by ICA and its applications.Furthermore,the chapter includes the main purpose and the main research of the paper.In Chapter 2,basic theories and methods of ICA are introduced.Different kinds of classic measures can be used for the estimation of ICA,such as kurtosis and negentropy,etc.In Chapter 3,the rational function ICA algorithm is presented which can blindly separate the super-gaussian and sub-gaussian signals from the mixture effectively.It applies a rational function directly to a nonlinear function instead of switching between sub-gaussian and supergaussian regimes.In addition,the nonlinear function chosen as the rational function in Fast ICA algorithm is discussed in the end.In Chapter 4,we compare the rational function ICA algorithm with the Extended Infomax algorithm in terms of performance and computational efficiency.Finally,we discuss the conclusion and prospection of this paper.