毕业论文
盲源分离算法研究与仿真
系 别 专业名称 班级学号 学生姓名 指导教师
电子信息系 通信工程 4050810 邵一洲 刘福来
2009年6月15日
东北大学秦皇岛分校毕业设计（论文） 第 I 页
盲源分离算法研究与仿真
摘 要
盲信号处理（BSP）是近年来现代信号处理领域研究的主要方向之一，其研究涉及人工神经网络、统计信号处理和信息论的有关知识，具有重要的理论价值，已经成为人工神经网络的主导发展方向之一。盲源信号分离（BSS）是用于解决从混合观测数据中分离源信号的一门新技术，已在许多领域获得了广泛应用。
本文首先介绍了盲分离问题的基本概念、数学模型、求解问题的关键以及信号盲分离中存在的不确定性因素。然后介绍了目前在信号忙处理中应用最广的独立分量分析（ICA）方法，总结出ICA的根本原理是通过分析多维观测数据间的高阶统计相关性，找出相互独立的隐含信息成分，完成分量间高阶冗余的去除及独立信源的提取。
本文的主体是基于独立分量分析的盲分离算法的仿真与实现。文中详细阐述了基于独立分量分析的快速定点（FastICA）算法和信息最大化（Infomax）算法的原理，通过算法原理总结出实现算法的步骤和流程。并利用上述两种算法对亚高斯混合信号，超高斯混合信号，以及亚高斯和超高斯杂系混合信号进行了仿真分离实验。最后在本文的结论中，对快速定点算法和信息最大化算法进行了总结，并对今后信号盲分离问题的研究工作的发展提出了一些看法。
关键词：盲信号处理；盲源分离；独立分量分析；FastICA算法；Infomax算法
东北大学秦皇岛分校毕业设计（论文） 第 II 页
Blind Source Separation Algorithm Research and Simulation
Author: Shao Yizhou Tutor: Liu Fulai
Abstract
Blind signal processing (BSP) is one of the main aspects which has been studied in the field of modern signal processing in recent years, it‘s involving the knowledge of artificial neural network, statistical signal processing and information theory. It has an important theoretical value and has become the leading development directions in artificial neural network. Blind Signal Separation is a new technology which separate source signals from mixed observational data, and it has gained widespread application in many areas.
This paper introduced the basic concepts, mathematical model, the key to solving the problem of blind signal separation, as well as the existence of uncertainties. And then introduced the most widely method - Independent Component Analysis, in the signal processing currently. The fundamental principles of ICA is through analysis of high-ranking statistical correlation between multidimensional observation data, find mutually independent implicit message content, complete removal of a high redundancy and independent sources extraction letter.
The main body of this article is the algorithm and implementation of simulation, based on independent component analysis of blind source separation. In this paper we elaborating the principle of fast fixed-point algorithm and information maximization algorithm based on ICA, summed up the steps and processes of algorithm. And successfully use these two algorithms to separate sub-gaussian signals, super-gaussian signals, and the mixture signals between these. Finally, in the conclusions of the dissertation, the FastICA algorithms and the Infomax algorithm are summarized, and the viewpoints for the future are proposed
Keyword: Blind Signal Processing; Blind Signal Separation; FastICA algorithm;
Infomax algorithm; Independent Component Analysis;
东北大学秦皇岛分校毕业设计（论文） 第 III 页
目 录
第一章 绪论 ............................................................................................................................ 1
1.1 盲信号处理研究的背景和意义 ................................................................................ 1 1.2 国内外研究历史及现状 ............................................................................................ 2 1.3 本文的研究内容及章节安排 .................................................................................... 6 1.4 章节安排 .................................................................................................................... 7 第二章 信号盲分离基本问题 ................................................................................................ 8
2.1 引言 ............................................................................................................................ 8 2.2 盲分离的概念 ............................................................................................................ 8 2.3 盲分离问题的描述 .................................................................................................... 9 2.4 混合模型 .................................................................................................................... 9
2.4.1 源信号的统计特征 .......................................................................................... 9 2.4.2 源信号的混合方式 ........................................................................................ 10 2.5 盲分离的数学模型 .................................................................................................. 10 2.6 信号盲分离的不确定性 .......................................................................................... 11 第三章 独立分量分析 .......................................................................................................... 12
3.1 引言 .......................................................................................................................... 12 3.2 独立分量分析的线性模型 ...................................................................................... 12 3.3 ICA问题中的基本假设 .......................................................................................... 13 3.4 对信号的预处理 ...................................................................................................... 14 3.5 独立分量分析独立性的度量 .................................................................................. 16
3.5.1 非高斯性极大 ................................................................................................ 16 3.5.2 互信息最小 .................................................................................................... 17 3.5.3 非线性不相关 ................................................................................................ 17 3.6 本章总结 .................................................................................................................. 18 第四章 基于独立分量分析的算法仿真与实现 .................................................................. 19
4.1 引言 .......................................................................................................................... 19 4.2 Infomax信息最大化算法 ........................................................................................ 19
4.2.1 Infomax算法原理 .......................................................................................... 19 4.2.2 Infomax算法仿真 .......................................................................................... 25 4.3 FastICA快速定点算法 ............................................................................................ 31
4.3.1 FastICA算法原理 .......................................................................................... 31 4.3.2 FastICA算法仿真 .......................................................................................... 34 4.3 分离算法的对比 ...................................................................................................... 42 4.4 本章小结 .................................................................................................................. 42 第五章 总结与展望 .............................................................................................................. 44
5.1 总结 .......................................................................................................................... 44 5.2 研究展望 .................................................................................................................. 45
东北大学秦皇岛分校毕业设计（论文） 第 IV 页
致 谢 .................................................................................................................................. 46 参考文献 .................................................................................................................................. 47 附 录 .................................................................................................................................. 49
翻译 ................................................................................................................................... 49
英文原文 .................................................................................................................... 49 中文译文 .................................................................................................................... 55 部分仿真程序源代码 ....................................................................................................... 60