Several Algorithms For Independent Component Analysis And Their Applications

Independent component analysis (ICA) is a new statistical signal processing technique for extracting independent sources given only observed data that are mixtures 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, telecommunications, face recognition, natural scenes, neural computation and medical signal processing, etc. This dissertation is devoted to the study of several algorithms for independent component analysis and their applications. The paper is organized as follows:In Chapter 1, we introduce in detail the status of independent component analysis in the aspects of algorithms and applications. In addition, we introduce the main research of my paper.In Chapter 2, a new fixed-point algorithm for independent component analysis (ICA) is presented that is able blindly to separate mixed signals with sub-and super-Gaussian source distributions. The new fixed-point algorithm maximizes the likelihood of the ICA model under the constraint of decorrelation and uses the method of Lee et al. (ExtICA) to switch between sub- and super-Gaussian regimes. The new fixed-point algorithm maximizes the likelihood very fast and reliably. This algorithm uses extended Infomax algorithm for accurate source separation and the fixed-point algorithm for a faster convergence. We compare the new fixed-point algorithm with two ICA algorithms (FastICA and ExtICA). The results show that the separation accuracy of the new algorithm is the best. And the new fixed-point algorithm is much faster than the ExtICA. Then, we perform the new fixed-point algorithm for fMRI experiment. As far as the temporal dynamics of the fMRI data is concerned, the new fixed-point algorithm is better than FastICA.In addition, concerning the inherent indeterminacy of ICA on dilation and permutation, we propose an algorithm for constrained independent component analysis based on projection methods. The projection methods and Lagrange multiplier methods are used to order the independent components in a specific manner and normalize the demixing matrix in the signal separation procedure. This can systematically eliminate the indeterminacy of ICA on permutation and dilation. The validity of the algorithms are confirmed by the experiments and results.In Chapter 3, blind source separation is discussed with more sources than mixtures when the sources are sparse (overcomplete ICA). The blind separation technique includes two steps. The first step is to estimate a mixing matrix, and the second is to estimate sources. The mixing matrix can be estimated by using a clustering approach which is described by the generalized exponential mixture model (or the sparse mixture model) whether the model is the noise free model or the low level noise model. The generalized exponential mixture model (or the sparse mixture model) is a powerful uniform framework to learn the mixing matrix for sparse sources. A gradient learning algorithm for the generalized exponential mixture model (or the sparse mixture model) is derived. After the mixing matrix is estimated, the sources can be obtained by solving a linear programming problem (the noise free model) or using the maximum a posteriori approach ( the low level noise model). The speech-signal experiments demonstrate effectiveness of the proposed approach.In Chapter 4, we consider the estimation of the ICA model when the independent components are time signals. A fixed-point algorithm for complexity pursuit is introduced based on the Kolmogoroff complexity. We search for projections that can be easily coded in the complexity pursuit. This is a general-purpose measure and is probably connected to information-processing principles used in the brain.ICA in its basic form ignores any time structure and uses only the nongaus-sianity criteria. And under certain restrictions, it is also possible to estimate the independent components using the time-dependency information alone. However, the complexity pursuit algorithm combin...