基于玻耳测度峰值判定的盲源分离方法

Blind Source Separation Based on Borel Measure Peaks

α-稳定分布可以更好地描述实际应用中所遇到的具有显著脉冲特性的随机信号和噪声.与其它统计模型不同,α稳定分布没有统一闭式的概率密度函数,其二阶及二阶以上统计量均不存在.本文先简要介绍稳定分布的特征函数及其玻耳测度表示,再提出了玻耳测度的估计方法,并利用玻耳测度的峰值确定混合矩阵的基矢量,从而可以确定各个独立分量,并能实现信号盲分离.计算机模拟和分析表明,这种算法是一种在高斯和分数低阶α稳定分布噪声条件下具有良好韧性的独立分量分析与盲信源分离方法.

Stable processes can better model the impulsive random signals and noises in physical observation. This class of process has no close form of probability density function and finite more than second order moments. This paper briefly introduces the statistical characteristics of stable distribution. In this paper, a new method for identifying the independent components of an alpha-stable random vector for under-determined mixtures is proposed. The method is based on an estimate of the discrete spectral measure for the characteristic function of an alpha-stable random vector. Simulations demonstrate that the proposed method can identify independent components and the basis vectors of mixing matrix in the so-called under-determined case of more sources than mixtures.