The Mathematical Theoryand Algorithms Of Underdetermined Blind Source Separation Of Signal

With the development of information and computer technique, in many applica- tions,the mixing signals or the mixing signals with noise of the source signals can be obtained by the sensors,how to separate the original source ignals from the mixing signals is the problem that must to be solved in some applications,the technique of blind source separation is being developed under this circumstance.This dissertation reviews the development of BSS,the current research status,the related theory. In this article, we analyze and summarize the previous work of blind source separation including classical algorithm and theory. Emphasis of this paper achieve no noise blind source separation by"two-step", with sparse representation. Here we have estimated on the assumption that A is known, focused on how to estimate the source signal s (t). The core of this problem is to establish the target function and design optimization algorithm. Under different circumstances, to establish different target function, thus design corresponding optimization algorithm. According to the different conditions of the underdetermined blind source separation, this paper studies two underdetermined blind source separation problems. One is only equality constraints of nonsmooth convex optimization problem, the other is a nonsmooth nonconvex optimization problem with a nonsmooth nonconvex objective function, a class of af?ne equality constraints, and a class of nonsmooth convex inequality constraints.To solve these kinds of problems, we develops a neural network which is modeled by a differential inclusion. It is proved the existence, uniqueness of the solutions. Suf?ciently large penalty parameters, any trajectory of the neural network can reach the feasible region in ?nite time and stays there thereafter. Moreover, under the first one ,the trajectory of the neural network converges to the optimal solutions set of the neural network. Under the second one, the trajectory of the neural network converges to the set consisting of the critical points.Finally, this paper contains two examples, which show the feasibility of the results in this paper.