The Algorithm Research On Sparse Component Analysis For Underdetermined Blind Source Separation

In practical applications, with the rapid development of sensingtechnique and signal processing technology, it is more often need to get allsorts of useful signal through sensors. However, these useful signals areusually mixed with other sources or noise. How to separate these usefulsignals from the hidden aliased is a difficult technical problem whichneeds to be solved urgently. Blind source separation technology isemerged in this context. The paper studies the problem of underdeterminedblind source separation(with less observed signals than sources). Based onthe sparse component analysis, a two-step strategy including theestimation of the mixing matrix and the recovery of sources is investigatedin the underdetermined blind source separation and three types of mixingmatrix estimation methods are summarized. In this thesis, a new mixingmatrix estimation algorithm based on ant colony clustering has beenproposed. In addition to this, a new sources recovery algorithm calling theweighted L1-norm minimization algorithm has also been proposed.The main research work of this paper as follows:(1) We study the two steps algorithm of the underdetermined blindsource separation. The paper has explained the main algorithms in themixing matrix estimation stage, such as the potential function algorithm,k-means and its improved algorithm, the hough transform algorithm.Simulation results show the performance of each algorithm. The shortestpath method in the source signal recovery stage has also been explained.(2)A new mixing matrix estimation algorithm is proposed in thispaper. Taking advantage of the straight line clustering of the sparse sourcesignals in underdetermined blind separation, the aliasing signals arestandardized and the aliasing signals are formed spherical cluster, so thelinear cluster is turned into density cluster. According to the distancebetween different observed signal points, The initial pheromone matrix isproduced and the initial cluster centers are found. And then the clusteringcenter is searched and obtained by using the ant clustering algorithm.Finally, the aliasing matrix are accurately evaluated.(3) A new sources recovery algorithm is proposed. First, the algorithm calculate the absolute difference in angle between the observedsignal vectors and the estimated mixing matrix column vectors accordingto a certain threshold. The observed signal vector potentialdecompositions have been got. And then, by combinating the potentialdecompositions, the weighted sum of the minimum L1-norm solutions aretaken as the estimation of the sources.