Some Algorithms For Independent Component Analysis And Their Applications To FMRI Data Analysis

Independent component analysis (ICA) is a new statistical signal processing technique for extracting independent component sources given only observed data that are mixtrues of the unknown sources. Recently, blind source separation by ICA has received great attention due to its potential signal processing applications such as speech signal processing, telecomminications, face recognition, natural scenes, neural computation and medical signal processing, etc. This thesis aims at performing ICA in the presence of Gaussian noise. Particularly, we perform ICA by maximizing data likelihood, and estimate the mixing matrix and noise covariance and infer the independent component sources by EM algorithms.Chapter two proposes an expectation-maximization (EM) algorithm for learning sparse and overcomplete representations which could perform blind source separation of more sources than mixtures. We show that the estimation of the conditional moments of the posterior distribution can be accomplished by maximum a posteriori estimation. The approximate conditional moments enable the development of an expectation-maximization algorithm for learning the overcomplete basis vectors and inferring the most probable basis coefficients.An EM algorithm for performing independent component analysis in the presence of Gaussian noise is presented in Chapter three. The estimation of the conditional moments of the source posterior can be accomplished by maximum a posteriori estimation. The approximate conditional moments enable the development of an EM algorithm for inferring the most probable sources and learning the parameter in noisy independent component analysis. Simulation results show that the proposed method can perform blind source separation of sub-Gaussian mixtures and super-Gaussian mixtures.Expectation-maximization (EM) algorithms for independent component analysis are presented in chapter four. For supergaussian sources, the proposed method develops variational approximation to a range of heavy-tailed distributions. This variational approximation derives a rigorous lower bound on the prior distribution which gives a normal form of a lower bound on the source posterior. This lower bound enables the development of an expectation-maximization algorithm for blind separation of supergaussian sources. Simulation results show that this EM algorithm can perform bind separation of moresources than mixtures and learn overcomplete bases for speech data. For subgaussian sources, a symmetrical form of the Pearson mixture model is employed as the subgaussian density, which also give a normal form of the source posterior. This normal form enables the development of an expectation-maximization algorithm for blind separation of subgaussian sources. This EM algorithm can perform blind separation of binary sources with less sensors than sources.The mathematical principles of analysis of functional neuroimages (AFNI) are discussed in Chapter five . This chapter introduces how to analyze fMRI data using decon-volution technique.Chapter six discusses how to analyze fMRI data by blind separation into independent spatial components. Since the functional magnetic resonance imaging (fMRI) signals from the experiments can be regarded as a specific problem of blind source separation, the FastICA algorithm can be considered as a method of extracting independent component maps from fMRI signals. Current analytical techniques applied to fMRI data require a priori knowledge or specific assumptions about the time courses of processes contributing to the measured signals. Without any priori knowledge about the time courses of processes contributing to the measured signals, spatial ICA is used to separate fMRI Data into task-related independent components?head movement independent components? transiently task-related independent components?noisy independent components and other independent component signals.