Application Of MP And BP Sparse Decomposition To Blind Source Separation

BSS(Blind Source Separation, BSS)(ICA(Independent Component Analysis, ICA))is one of popular research topics in signal processing. SCA (Sparse Component Analysis, SCA) gradually becomes a new research aspect in the BSS. In fact, there are some relations between SCA and ICA, because there are the following potential in ICA, such as de-noising, date compress and character distil and so on. It is used in ICA as a complementary condition and is a significant processing method. This thesis presents the SR(Sparse Representation, SR)principle of MP(Marching Pursuit, MP) and BP. (Basis Pursuit, BP). What is more, MP and BP is used in blind source separation of signals, images and time-frequency domain. The thesis can prove through experiment that there are widely prospects in the SCA used in BSS. The major task in this paper is as follows:1. In the research of ICA, "Enhancing the Gaussian distribution utmost" and "enhancing the source more sparsely" are coincident. MP and BP Sparse representations are the problem of sparse representation based on over-complete dictionary of atoms. This thesis uses them to reconstruct the mixed-signal of SR, and uses joint distribution for experimental simulation. The result shows that the effect of joint distribution is much better. The feasibility of application of MP and BP sparse decomposition to blind source separation is proved.2. According to feasibility analysis as above, this thesis studied the MP sparse decomposition blind source separation arithmetic based on kurtosis and the BP sparse decomposition blind source separation arithmetic based on maximum SNR. MP and BP are separately used in blind source separation. We can come to the conclusion from the experiment that this algorithm has a better separating effect.3. The thesis applies MP sparse decomposition in image blind separation algorithm, which made this process more complex and instable compared with one-dimensional signals due to the fact that image signal is effected by two-dimensional correlation. This thesis attempts to apply the maximum SNR image blind separation method based on the MP sparse decompose, so that the stability of sparseness can make the separation of blind imagines have better simulation results.4. Sparse blind source separation is a SCA method based on transform domain. In transform domain, there exist other interferes, such as crosstalk interference in time-frequency domain. In order to solve this problem, this thesis studied the MP sparse decomposition blind source separation arithmetic in time-frequency domain. That MP denoises makes this research meaningfulness. The result indicated that this algorithm has a better effect.