Study On Independent Component Analysis Algorithms And Their Applications With AR Source Model

Independent component analysis(ICA) is a new data processing and analysis technique for extracting independent sources given only observed data that are mixtures of unknown sources.Recently,blind source separation by ICA has received great attention due to its potential signal processing applications such as speech signal processing, telecommunications,face recognition,image feature extraction and medical signal processing, ect.This dissertation is devoted to the study of several algorithms for temporal independent component analysis and their applications by using AR source model.The main achievements are as follows:1.The algorithms of noise-free independent component,analysis with AR source model were studied.The log-likelihood of the model is derived in detail when each source is a first-order AR model,then the ICA learning algorithms are proposed in three cases.(1) A gradient algorithm is given by maximizing log-likelihood of the model when the probability density function of innovation is generalized Gaussian distribution; (2) There are many parameters in the gradient algorithm,and the functions are complexity.So we use a nonquadratic function approximate the logarithm of the probability density function of the innovation process,a batch and an on-line algorithms are introduced and their theoretics analysis are carried out simultaneously.Computer simulations show that the algorithms can separate mixed signals,and the batch algorithm can separate mixed images and.achieve better separation effect;(3) There is a learning rate in the batch algorithm which influenced the convergence speed.In order to overcome drawback:a fixed-point algorithm is derived using approximate Newton method by maximizing log-likelihood function of the model.Computer simulations verify the fixed-point algorithm converges faster than the batch algorithm and it is easy to implement due to it does not need any learning rate.2.The algorithms of noisy independent component analysis with AR source model were studied when the noise covariance is known and the noise covariance is unknown. When the noise covariance matrix is known,a fixed-point algorithm is proposed by maximizing the negentropy of innovation.Computer simulations show that the fixedpoint algorithm converges faster than the existing gradient algorithm,and can separate the mixed images and achieve better separation effect.When the noise covariance is unknown,an improved gradient algorithm and a new noisy algorithm are introduced to estimate the mixing matrix and noise covariance matrix simultaneously.Computer simulations verify the two algorithms can separate the mixed signals.Comparison results show that the new noisy algorithm converges faster than the improved gradient algorithm,and it is easy to implement due to there is only one learning rate to be chosen.3.The algorithm of noise-free independent component analysis were studied with AR source model and nonstationary variances.In 2005,the log-likelihood of the model was given and a gradient algorithm was proposed by maximizing log-likelihood of the model by Hyv(a|¨)rinen.But the convergence speed is influenced by the choice of the learning rate.In order to overcome this drawback,a fixed-point algorithm is proposed using approximate Newton method by maximizing log-likelihood of the model.Computer simulations show that the fixed-point algorithm converges faster than the gradient algorithm,and it is more implement due to it does not need any learning rate.4.The algorithms of noisy independent component analysis were studied with AR source model and nonstationary variances when the noise covariance matrix is known and the noise covariance matrix is unknown.When the noise covariance matrix is known, the log-likelihood function of the model is given by using the property of Gaussian moments and a gradient algorithm is introduced by maximizing the log-likelihood function of the model;when the noise covariance matrix is unknown,a new gradient algorithm is introduced by developing the gradient algorithm to estimate unmixed matrix and noise covariance matrix simultaneously.Computer simulations show that the two algorithms can separate the artificial mixed signals and achieve better separation effect.5.The algorithms of blind extraction of FECG with AR model were studied.A new gradient algorithm is given using approximate Newton method by minimizing objective function when Gaussian noise is not present.Computer simulations show that the algorithm can extract FECG from the artificial signals and the real-world ECG data:When Gaussian noise is present in the model,an objective function is given by utilizing the property of Gaussian moments,and a gradient descent algorithm is proposed.Computer simulations verify the gradient,descent algorithm is effective and feasible.