Research On Blind Source Separation Based On Morphological Component Analysis

Blind source separation refers to the condition of the signal source and the priori information of the transmission system is lacking or unknown, based solely on the observation of sampled sensor signals to estimate signal sources. Recently, it’s an important subject in the field of signal and information processing. Morphological component analysis theory is proposed based on theory of sparse representation. The theory assume that the signal is a linear combination of several components having different geometry, and each embodiment of the component can be sparsely represented in a dictionary, and not sparse representations of the others. In recent years, this theory has been applied to solve the blind source separation problem and obtained good results.This thesis describes the theoretical basis of sparse representation and sparse decomposition algorithm such as OMP and BP. Morphological component analysis assume that the source signal meets sparsely and morphological diversity. Then, this thesis gives a decomposition algorithm based on block coordinate relaxation component analysis. Currently, sparse representation dictionary is selected by experience in image processing fields, and therefore we introduce several common sparse representation dictionaries for the image of the cartoon and texture parts.Morphological component analysis in blind source separation applications has two main models: multi-channel morphological component analysis(MMCA) and generalized morphological component analysis(GMCA). The multi-channel component analysis algorithm is only suitable for the source signals, which have a single morphological component, and the generalized morphological component analysis algorithm is an extension of the multi-channel morphological component analysis for solving the MMCA model. Finally, simulations by using the multi-channel component analysis, generalized morphological component analysis and fast independent component analysis(Fast ICA), and the results show that morphological component analysis in solving the problem of blind signal separation model has better separation performance and robustness than the fast component analysis.The recent results of the ESA/Planck space mission in 2013 have shed light on the crucial role that blind source separation has played to provide a very accurate map of the Cosmological Microwave Background from multi-wavelength microwave data. These components are, by nature, partially correlated. Disentangling among the different galactic sources is a challenging task, which has been rarely tackled by using blind source separation so far. Generalized Morphological component analysis does not consider the correlation between the signal source, so to solve this issue has some shortcomings, this thesis proposes the correlation between the signals will be re-added to the algorithm residuals step for improving the original algorithm. Numerical simulation experiments show that in the case of a light correlation between the signal source, the improved algorithm similar performance than the original algorithm in the absence of noise or low noise. At high noise environment, the improved algorithm has better robustness and stability than the original algorithm. When the signal source is partially correlated, the improved algorithm has better robustness and separation performance than the original algorithm, the performance improved by at least 10%. Therefore, the improved algorithm will have a good application for obtaining the Cosmological Microwave Background in the field of astronomy.