【作者】 宋娟；

【导师】 薛小平；

【作者基本信息】 哈尔滨工业大学 ， 基础数学， 2010， 硕士

【摘要】 随着信息和计算机技术的发展,很多实际应用中通过传感器获得的是一些有用信号的混叠信号或带噪声的混叠信号,如何将这些隐藏在混叠信号中的原始信号分离出来,是一些应用中必须解决的问题,盲源分离技术正是在这种背景下应运而生的。本文系统回顾了盲源分离技术的发展历史、研究现状,在总结盲源分离理论基础及经典算法的基础上,研究了欠定盲源分离技术相关理论。本文的重点是借助稀疏表示,采用“两步法”实现无噪声欠定盲源分离。这里我们在假定A已经估计出来的前提下,集中研究如何估计源信号s (t).此问题的核心就是:建立目标函数和设计优化算法。从不同的角度,在不同的情况下(如源信号是否独立同分布,源信号服从哪种分布等),建立不同的目标函数,从而设计相应的优化算法。根据欠定盲源分离的不同情况,本文研究了两种欠定盲源分离问题。一种是只有等式约束的非光滑凸优化问题;另一种是既有等式约束又有不等约束的非光滑非凸优化问题。在解决这两类问题时本文采用以微分包含为模型的神经网络,得出解的存在性、唯一性,以及在参数足够大时,神经网络的轨道在有限步内达到可行域并且永驻其中。同时,本文还得出非光滑凸时轨道收敛到最优解集,而非光滑非凸时收敛到临界点集。最后本文给出两个算例,进一步验证本文结论的可行性。更多还原

【Abstract】 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.更多还原