一种独立成分分析的鲁棒算法及其在脑磁图数据分析中的应用

独立成分分析是一种新的信号处理统计方法。被广泛用于各个领域。在信号分析中面临的难题是：源信号的不同特性（既包括超高斯信号又包括亚高斯信号）；未知的独立源数目；传感器信号受到较大的加性噪声污染。针对以上难题，本文提出了一种独立成分分析的鲁棒算法。该方法先对观测数据作预处理，将包含噪声的高维传感器观测信号降维分解到信号子空间和噪声子空间。利用交叉验证法估计出独立源的数目（解决了独立成分分析本身不能确定源数目的缺陷）；然后利用快速稳定的FastICA算法分离独立成分。通过人工合成的数据和实际的脑磁图数据分析。验证了这种方法的功效。

A Robust Approach to Independent Component Analysis and Its Application in the Analysis of Magnetoencephalographic Data

Independent component analysis(ICA) is a new method of signal statistical processing and widely used in many fields.We face several problems such as the different nature of source signals(e.g.both super-Gaussian and sub-Gaussian sources exist),unknown number of sources and contamination of the sensor signals with a high level of additive noise in the analysis of signal.A robust approach was proposed to solve these problems in this paper.Firstly,observations(noisy data) possessing high dimensionality were preprocessed and decomposed into a source signal subspace and a noise subspace.Then the number of sources was got through the cross-validation method,and this solved the problem that ICA could not confirm the number of sources.At last the transformed low-dimensional source signals were further separated with the fast and stable ICA algorithm.Through the analysis of artificially synthesized data and the real-world Magnetoencephalographic data,the efficacy of this robust approach was illustrated.