The Theory And Application Of Blind Source Separation ICA

Blind signal separation(BSS) is the basic problem in the research of signal processing. BSS algorithms are also applied in data analysis and data mining. If the original sources are statistically mutual independent, independent component anal-ysis(ICA) is a fundamental tool in theoretical research and practical applications such as signal processing, telecommunications, speech processing, and biomedical signal analysis where multiple sensors are involved. The research areas of ICA include noisy ICA algorithms, the fundamental ICA algorithms and their convergence analysis, over-complete and over-determined ICA models and their applications. Although in the practical application, the mutual independence of components is possibly too strict, both of its theoretical research and application in the speech recognition, telecommunication and medical signal processing, ICA is becoming more and more important.On the other hand, BSS of signal and image processing is considered as matrix factorization. For this type of BSS algorithms, sources are generally assumed to be statistically dependent, and additional constraints such as nonnegativity, sparsity, smoothness, lower complexity or better predictability are imposed to the cost function. We express the non-negativity constraints using a wide class of loss(cost) functions, which leads to an extended class of multiplicative algorithms with regularization. These algorithms are called non-negative matrix factorization (NMF). Algorithms for NMF is promising in applications to blind source separation. But the global convergence of the proposed algorithms are hard to analyze.In this thesis, as a review, the existing BSS algorithms are introduced first. Then, the convergence of a generalized NMF algorithms are analyzed. From the analysis, the convergent areas are obtained. Based on regression ICA and image reconstruction algorithms, some new algorithms for noise ICA and overcomplete ICA are proposed. The simulations and contrast with other algorithms show that the new algorithms have good test results.The application of ICA to cashflow and meteorological independent components analysis is also discussed. We first construct models for the applications, and then based on the real data, these models are tested. The test results show that our models are very effective on data analysis and predictions. The application studies show the interesting relation between ICA and data mining.In the thesis, Chapter 1 is the introduction part, in which the most important BSS algorithms and their application in signal processing and data analysis are described. In chapter 2, based on Amari's alpha divergence, a non-negative matrix factorization algorithm is introduced. In this part, the stability of the algorithm is analyzed. The analysis shows the convergence of the algorithm can be guaranteed in some predefined conditions. In Chapter 3, regression ICA is employed to construct a new algorithm for image denoising and signal processing. Experiments demonstrate that the proposed algorithm can separate different signals and images from their mixtures where different types of noise are added to the original sources. In Chapter 4, image space reconstruction algorithm and regression ICA are employed to construct a new algorithm for the estimation of overcomplete ICA and the stability and convergence conditions are also analyzed. Experiment shows that mixed speech signals can be separated with good fidelity. In Chapter 5, based on the Fast ICA algorithm, a model for chain stores' sales is set up. Using this model, we can analyze the distributions of the sold products from the online cashflow in each store of the chain. This model will be very attractive to provide information for making their future sales plan. In Chapter 6, BP based time series ICA algorithm is employed for the analysis of meteorological data, from which some hidden independent components in the observations can be estimated. The estimated independent components can be further used to predict the future observations of the meteorological data. Chapter 7 is the extension of Chapter 2, in which the convergence of the Kullback-Leibler(KL) divergence based BSS algorithm is analyzed and from which the convergent areas are obtained. Chapter 8 is the summary of the thesis and it also gives some prospects of BSS for the future research.