Blind Source Separation Based On Sparse Reprensentation And Its Improvement

Blind source separation is recently hottest topics. It obtains abroad development inmany field especially in sonar system, rada system, biology signal processing, imageprocessing, speech signal processing, etc. It catch more and more attentions ofscientific researchers.What is called "blind", i.e. we only know the observation signal without priorinformation of sources and its transmission channels. So estimating the independentsources only from the observation is the task of blind source separation(for shortBSS).The number of mixtures is not less than that of the sources in general BSS whichcan be transformed to be a inverse problem of mixture system. Moreover, when thenumber of sources are more than that of observation which is called "undeterminedblind source separation", the inverse system is not exist. furthermore, the estimationsources are not unique even if the mixture system has been known. So we firstly needto estimate the mixture system and then estimate the sources.In this paper, we take emphasis on the undetermined blind separation of linearinstantaneous mixtures of source. A two-step BSS algorithm base on sparserepresentation of signal will be discussed . And wavelet transformation is also used inthe algorithm. In the first step, we estimate the mixture matrix by k-means clustering inthe wavelet transformation domain. And then estimate the sources by the estimatedmatrix(basis matrix) and sparse-processed mixing matrix(data matrix) in the secondstep. We firstly discuss the separability of the blind sources based on sparserepresentation under the probability frame, and set up a group of probability inequalityand probability estimation which is indicate the connection of separability and numberof observation, the number of sources, the sparse degree of sources. In the end, weimprove the algorithm from two ways. One is the improvement of k-means clusteringalgorithm, the other is the shortest road algorithm which can estimate sourcesefficiently. We choose three sparse images to mix and separate it using the improvedalgorithm. We found that the improved algorithm could not only largely reducecomputation but obtain good separation purpose.Finally, sum up this paper and discuss the further research and potential application.