Research On Kernel Independent Component Analysis Algorithms In Blind Source Separation

Blind Source Separation (BSS) refers to the process that separating source signals frommixed observation signals under the condition of either theoretical models or source signalscan not be accurately obtained. Independent Component Analysis (ICA) is one of the mostimportant methods to solve BSS problems. As a semi-parametric model, the key to solutingICA is the selection of specific nonlinear empirical contrast functions, while the existing ICAalgorithms often have limitations. By the mapping of kernel functions, kernel methods whichsolute problems in feature space have agile nonparametric characteristics, and more accurateand robust results can be obtained when kernel method is used to solve BSS problems.Meanwhile, the selection of kernel functions has a great influence on kernel methods.Wavelet kernel functions have the characteristics of approximate orthogonality and theadvantage in local signal analysis. Ideal mathematical properties can be obtained when kernelgeneralized variance (KGV) which makes analysis in the global spectrum range is treated asthe contrast function. Combining with both advantages, this thesis presents a wavelet kernelgeneralized variance kernel independent component analysis (WKGV-KICA) algorithm. Thealgorithm is applied to a wide range of BSS problems and its effectiveness has been verified.The main contents of this thesis are as follows.(1) Theoretical research has been applied to the data pretreatment process and theclassical ICA algorithms by maximization of nongaussianity, maximum likelihood estimationand minimization of mutual information.(2) Based on systematical studying of canonical component analysis (CCA) andinformation theory, theoretical research has been applied to the KICA algorithms based onKernel Canonical Component Analysis (KCCA) and KGV. Meanwhile, by constructingtranslational invariance wavelet kernel functions, combined with KGV theory, a new WKGV-KICA algorithm is put forward.(3) WKGV-KICA algorithm is applied to the detection of multi-sources sensor system,separation of mixed voice signals, recovery of image signals and detection of fetalelectrocardiogram (FECG) such four wide range BSS experiments. With comparisons ofperformance indicators, the effectiveness of WKGV-KICA algorithm is verified.(4) WKGV-KICA algorithm is applied to the feature extraction of multi-spectral remotesensing images. Under the condition of the same extracted bands, WKGV-KICA can reservemore information of original images to improve the accuracy of target classification of remotesensing images, and the advantage of the algorithm has been further verified.