Research On Several Algorithms For Extended Independent Component Analysis And Their Applications

Independent component analysis(ICA) is a new promising method for data processing and analysis.The aim of the ICA is to extract original independent components from observed data that are mixtures of the unknown sources without any knowledge of the mixed channel.Recently,ICA has received great attention due to its potential signal processing applications such as speech signal processing,biomedical signal processing,neural computation,image feature extraction,telecommunications and face recognition etc.Due to its wide and attractive applications,many researchers have studied ICA in the past twenty years and made this technique considerable developed.However,ICA is still in an initial stage of development,some problems about its theory and application need to be enhanced and improved further.In this dissertation,we first provide an introduction about the research status and applications of ICA both at home and abroad.Then,preliminary knowledge of basic and extended ICA are given.In addition,some problems of extended ICA,for example,the ordering of independent components,the blind extraction of one or a set of interesting signals and the noisy blind source separation,are investigated deeply and several novel efficient methods are proposed.The main works in this dissertation can be introduced as follows:1.Based on the constrained independent component analysis model,we propose a method for eliminating the indeterminacy on permutation of the ICA.Most Of traditional ICA algorithms only exploit the direction of independent components but ignore these inherent indeterminacy,which is considered as unimportant impact factors in the signal processing.However,in many special applications,this inherent indeterminacy needs to be determined.Concerning this case,we propose an algorithm for constrained independent component analysis model based on projection methods and incorporate the new fixed-point(NewFP) algorithm into this constrained ICA model to construct a new constrained fixed-point algorithm.This method is applied to order the independent components in a specific statistical measures.Moreover,it is more simple to implement than other existing algorithms due to its independence of the learning rate.Computation simulations on synthesized signals,speech signals and real-world fetal electrocardiograph (ECG) data demonstrate that this method not only systematically eliminates the indeterminacy of ICA on permutation but also performs better.2.We further study the issue of blind source extraction(BSE) on temporal ICA (TICA) and present two BSE algorithms for extracting the desired signal with temporal structures.Firstly,through combining the generalized autocorrelations of the desired signal and the non-Gaussianity of its innovations,we develop an objective function,which is formulated as the convex combination of these priori special temporal characteristics.Maximizing this objective function,we obtain an efficient gradient BSE algorithm and further give its stability analysis in this paper.Note that ICA with its basic form ignores the time structure and uses only the non-Gaussianity criteria.However,the proposed algorithm combines both of these estimation criteria(non-Gaussianity and time-correlations) in order to exploit the data information as much as possible.Simulations on image data and ECG data indicate its better performance.Secondly,based on the temporal characteristics and other prior information of desired signals,we develop an objective function for extracting the interesting signals,which combines the generalized autocorrelations and reference information of desired signals. Maximizing this objective function,a BSE fixed-point algorithm is proposed.Comparing with other BSE method,this method makes full use of more priori information of the desired signal.It should be pointed out that the good performance of the proposed algorithm may attribute to the application of a properly reference signal.Fortunately, the proposed method does not excessively depend on the selection of the reference signals, which generalizes this method for broader applicability.Simulations on artificial ECG signals and the real-world ECG data demonstrate the better performance of the new algorithm.3.We study the problem of extracting or separating source signals with temporal structures.Moreover,we propose two noisy algorithms based on these priori special characteristics and Gaussian moments.Firstly,we address the extraction of the noisy model based on the temporal characteristics of sources.An objective function,which combines Gaussian moments to generalized autocorrelations,is proposed.Maximizing this objective function,we present a fixed-point noisy blind source extraction algorithm,which is given by bias removal techniques.This means that ordinary(noise-free) ICA methods are modified so that the bias due to Gaussian noise is removed,or at least reduced.Comparing with other existing extraction algorithms,the proposed algorithm shows its robustness to the estimated error of time delay even to high noise level.Simulations on synthesized signals,images and ECG data demonstrate the better performance of the proposed method.Secondly,we present a noisy blind source separation algorithm which incorporates Gaussian moments into the nonlinear innovation of original sources.This method is applicable to the situation when the noise covariance is known and source signals are nonstationary in the sense that the variance of each is assumed to change smoothly as a function of time.Furthermore,this method is extended to the case of noise covariance unknown in advance.Validity and performance of the described approaches are demonstrated by computer simulations.