【作者】 李蕾；

【导师】 张池平；

【作者基本信息】 哈尔滨工业大学 ， 计算数学， 2009， 硕士

【摘要】 盲源分离(BSS)是一种多维信号处理方法,它是指在源信号以及混合模型都未知的情况下,仅从观测信号中恢复出源信号各个独立分量的过程。盲源分离己成为现代信号处理领域研究的热点问题,在通信、语音处理、图像处理、地震勘探、生物医学、雷达以及经济数据分析等领域具有非常重要的理论意义和广泛的应用价值。本文提出了新的盲源分离算法,并给出了算法在图像分离中的应用。本文所做的主要工作:(1)从盲源分离的理论出发,由盲源分离问题引出独立成分分析。阐述了独立成分分析的发展历史和研究现状,以及在独立成分分析研究中存在的问题。(2)对独立成分分析理论基础进行了简单描述,讨论了独立成分分析研究中的主要问题。包括独立成分分析的数学定义、基本假设、相关的数学理论基础和实现途径等。(3)介绍和推导了基于独立成分分析的盲源分离算法的几种典型的学习算法,重点研究了FastICA算法。FastICA算法基于非高斯性最大化原理,使用固定点迭代理论寻找非高斯性最大值,采用牛顿迭代算法对观测变量的大量采样点进行处理,每次从观测信号中分离出一个独立分量,是独立成分分析的一种快速算法。(4)分别提出了基于简化牛顿法和修正牛顿法的算法,并给出了具体的实现步骤,将两种算法通过仿真试验进行了对比,实验结果表明,基于修正牛顿法的算法要优于前者。该算法减少了运算量,而且能够很好地分离出各个独立成分。最后计算机仿真验证了基于修正牛顿法的极大似然估计盲源分离算法在图像分离方面的有效性。更多还原

【Abstract】 Blind Sources Separation (BSS) is one of the multiple signals processing method; it is the process of recovering unknown independent source signals from sensor measurements which are unknown combinations of the source signals. BSS has become a hot topic of modern signal processing, so it has very important theory significance and utility value in communication , speech processing , image processing, biomedicine and radar technology, and it even can be applied to financial data analysis.This paper studies new algorithm and its applications in image separation. The major contribution of this paper is summarized as follow:1. BSS theories are firstly presented, and then Independent Component Analysis (ICA) is derived from BSS. Introduce the development history and the current research status of ICA, and the problems existed in ICA study.2. Simple mathematical preliminaries in ICA technique were given,main problems of the research of ICA are discussed, including the mathematical definition of ICA,the assumptions made about ICA problems and the mathematical theory and methods commonly used in ICA, etc.3. Several classical algorithms of BSS based on ICA and their derivations are introduced. Further, the FastICA algorithm is studied. FastICA is a fast algorithm of ICA, which is based on Fixed-point iteration theory to fix the non-Gaussian maximum. FastICA algorithm processes a large amount of sample point of received signals via Newton iterative algorithm, and recovers one independent component from the receiving signals one time.4. Introduce two algorithms based on Simplified Newton Method and Improved Newton Method, and compare these two algorithms through experiments. The experiment results prove the advantages of the algorithm which is based on Improved Newton Method, The algorithm reduces computation. It also separates independent components very well. Finally, computer simulations illustrate that the Maximum Likelihood Estimation algorithms based on Improved Newton Method can well separate mixed images.更多还原