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基于独立分量分析的盲信号分离算法研究
Research on the Algorithm of Blind Signal Separation Based on Independent Component Analysis
【作者】 程瑶;
【导师】 季策;
【作者基本信息】 东北大学 , 通信与信息系统, 2010, 硕士
【摘要】 盲信号分离(Blind Signal Separation,BSS)是近年来兴起的一个新的研究领域,独立分量分析(Independent Component Analysis,ICA)作为盲信号分离的一种有效方法而受到广泛的关注,在许多应用领域发挥着越来越重要的作用。在不知道源信号和混合矩阵的情况下,只需假设源信号是独立的,独立分量分析算法就能够很好的解决盲信号分离问题。本文的主要工作围绕着独立分量分析算法展开,对它进行了研究。本文介绍了ICA问题的发展历史、研究现状和实际应用,并对独立分量分析理论基础进行了简单描述,包括独立分量分析的数学定义、基本假设、相关的数学理论基础和实现途径等。讨论了几种独立分量分析的算法及其特点,并通过计算机仿真分析了快速算法(FastICA)的优越性。在独立分量分析算法的预处理中,研究了中心化和白化处理方法,并通过仿真实验证明了白化理论的正确性。着重研究了独立分量分析算法中的快速算法。对现有的快速算法进行了改进,提出了基于负熵的改进算法和基于四阶累积量的改进算法。在基于负熵的算法改进中,在分析FastICA算法的核心迭代过程的基础上提出了改进算法I-FastICA,改善了算法的收敛性能,减少了算法的迭代次数;针对I-FastICA算法的收敛依赖于初始权值的问题,在算法过程中加入松弛因子,提出LI-FastICA算法,改善了算法对初始权值的依赖性。在基于四阶累积量的改进中,以四阶累积量判据分析了传统的快速算法,然后用改进牛顿迭代法取代传统的FastICA算法的迭代步骤,提出了M-FastICA算法。将两种改进后的算法分别作图像信号和波形信号的仿真实验结果对比,数据显示了改进算法的性能有着较大的提高。在本文的最后,对全文进行了总结,并指出今后的研究方向。
【Abstract】 Blind signal separation (BSS) is a new research field recently rising and as a an effective method for the separation of blind signals, Independent Component Analysis(ICA) has attracted broad attention and becomes more and more important while using in wide fields. Under the condition without knowing the source signals and the mixing matrix, independent component analysis can solve the problem of blind signal separation soundly with the simple assumption that the sources are mutual independent. The work of this thesis is extended from independent component analysis algorithm.In this paper, after a brief introduction to the development history and current research status and applications of ICA, simple mathematical preliminaries of ICA technique was given, including the assumptions made about ICA problems, mathematical definition, the mathematical theory and methods commonly used in ICA, etc. Among the prime process of independent component analysis, centering and whitening was studied. At the same time, images simulations showed the effectiveness of the whitening theory.The basal theory and method of ICA algorithm and its fast algorithm (FastICA) was introduced. I-FastICA was advanced based analyzing kernel iterate course of the FastICA algorithm. I-FastICA improved convergence performance and reduced iterations. Aimed at the convergent speed of I-FastICA was dependent on initial weights, LI-FastICA was advanced by imported loosen factor, and reduced the dependence on initial weights. A modified fast ICA algorithm based on four-order cumulant was studied. Using the four-order cumulant as criterion, we analysised the traditional fast ICA algorithm; then proposed a new modified fast ICA algorithm which replaceed the iteration steps of fast ICA algorithm by improved Newton iteration method. Compared with two kinds of algorithm’s results on wave signals and imagin signals simulations, dates showed the validity of the modified algorithm.At the end of this paper, we give conclusions and introduce our future works.
【Key words】 Independent Component Analysis; Blind Signal Separation; Whiten Process; Negentropy; FastICA Algorithm; Loosen Factor; Four-order Cumulant;