| Sparse Component Analysis (SCA) is a kind of powerful Independent Component Analysis (ICA) based Blind Signal Processing (BSP) approach. It has been widely used in many fields, such as telecommunications, audio signal separation, biomedical signal processing, and image processing. A lot of SCA algorithms were proposed during the past few years. SCA has become one of the most attractive topics both in the fields of signal processing and artificial neural networks.However, most of SCA approaches assume that the source signals are sparse enough, this is a limit for practical application of SCA. In this thesis, the principle and algorithms of SCA for the non-sparse signals are explored based on Contourlet sparse representation, including the separation performance, initialization method and noise immunity. The underdetermined SCA approaches are also discussed and the proposed algorithms are applied to image separation.The main contributions of this thesis are as following:1) To improve the separation performance, a determined SCA approach based on Contourlet sparse representation is presented. The received images are decomposed into sets of sparse sub-images by the Contourlet transform, and the sparsest sub-images are selected to estimate the un-mixing matrix, then the source images are recovered by multiplying un-mixing matrix and the mixed images in space domain. Because the selected sub-images are sparser than the source images, the precision of the proposed approach is higher and its convergence speed is faster. Furthermore, since sparseness of image is usually space variable, a determined SCA approach based on block-wise Contourlet transform is proposed. The sub-images in Contourlet domain are blocked to get much more sparse ones with smaller size, and the separation performance of this approach is improved. The experiments results show that all these techniques are effective.2) To overcome the drawbacks that all the BSS algorithms are sensitive to the initialization settings, a kind of SCA initialization methods based on sparse representation are proposed. The received images are sparsed by wavelet transform, wavelet packet transform and Contourlet transform respectively. According to the distribution of the sub-images and the column vectors in mixing matrix, the sparsest sub-images are selected to estimate the mixing matrix. The proposed approaches are able to obtain higher separation performance with faster convergence speed. The simulation results confirmed the validity of the proposed methods. 3) A kind of noise immunity SCA techniques based on sparse representation are proposed. Firstly, the received images are de-noised in Contourlet domain by two kinds of de-nosing operators—Bayes estimation operator and Mathematical Morphology operator. Next, the sparsest sub-images are selected to get a more precise estimation of separation matrix by an improved sparse sub-image selection method. Based on this estimation and the de-noised mixed images, the separation results will be easily obtained and the source images are recovered lastly by further de-noising. The effectiveness of these approaches was shown by the simulation results.4) An underdetermined SCA approach is explored by using Contourlet sparse representation. The received images are sparsed by Contourlet transform, and a few couple of sparsest sub-images are used to estimate the number of source by counting its peaks in phase distribution. With the estimated source number, the mixing matrix is easily estimated through the clustering algorithm. Then the source images will be recovered by the basis pursuit approach. Compared with the traditional SCA, the proposed approach is more robust because it doesn't need to have the information about the source number in advance. The following simulation results showed its correctness and effectiveness.The principle and algorithms of SCA under the non-sparse condition are studied in this thesis. It expands the application of SCA with practical and theoretical significance.
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