Research On Underdetermined Blind Source Separation Of Speech Signals Based On Sparse Representation

Signal processing plays an important role in various fields and with the development of mobile communication and the geological prospecting technology, a new kind of signal processing is in an urgent need, then blind signal processing arises at the historic moment. Blind source separation is developed as a new kind of signal processing method 1990s, which has important theoretical value in researching the speech enhancement, the image recognition, the bioengineering signal, communication signals, and seismic exploration.Traditional blind source separation is always based on the assumption that the sensor number is more than source number, but with the further research of blind source separation more attention has been paid to underdetermined blind source separation which is more conform to the fact and would be more challenging. In this condition the system is irreversible, so the traditional blind source separation algorithm would fail. In this paper, based on sparse representation of speech signal, the key technologies of underdetermined blind source separation are explained.In this paper, the development status of blind source separation is briefly introduced firstly. Then explorative study is made on theoretical basis and key technology of the underdetermined blind source separation. the basic algorithms are also discussed. "Two-step" algorithm cluster-then-optimization to estimate the mixing matrix and source signals separately is a hotspot of underdetermined blind source separation, and it has close relation with signal sparse representation and overcomplete basis. This paper mainly studies the content as follows:Based on the sparse representation of signals, the fuzzy C-means clustering algorithm whose theoretical basis is most mature among pattern recognition clustering theory is applied to estimate the mixing matrix here. It can overcome the disadvantage of traditional potential function algorithm used to estimate the mixing matrix, such as complexity in the parameter selection and lack of theoretical guidance to define the potential function. But fuzzy C-means clustering is sensitive to the initial value and easy to be trapped in local optimum, so it will be combined with the differential evolution, named DE-FCM algorithm to realize unsupervised clustering, simple parameter selection, fast convergence rate, more accurate estimation and achieve global optimization finally. After getting the mixing matrix estimation, in order to estimate source signals with different degree of sparsity, this paper proposed a method based on the smoothed l0 norm to recover the source signals. Here minimum norm l1 method is no longer used, because minimize l1 norm can get a good result only when the signals are sparse enough. The method based on the smoothed l0 only uses an approximate function to approximate l0 norm directly and the quality of the approximation depends on a parameter called control factor. Experiments show that this method can get good result and the result can fit the mixing model better.