论文标题
混合光谱源的非参数独立组件分析
Nonparametric Independent Component Analysis for the Sources with Mixed Spectra
论文作者
论文摘要
独立组件分析（ICA）是一种盲目分离方法，可从其混合物中恢复感兴趣的源信号。大多数现有的ICA程序都采用独立抽样。基于二阶统计的源分离方法是基于来自自相关源的混合物的参数时间序列模型开发的。但是，当源具有与混合光谱的时间自相关时，基于二阶统计的方法无法准确地分离来源。为了解决此问题，我们通过分别使用立方花键和指标函数估算源信号的频谱密度函数和线光谱提出了一种新的ICA方法。混合光谱和混合矩阵是通过最大化晶体可能性函数来估计的。我们通过仿真实验和脑电图数据应用说明了提出方法的性能。数值结果表明，我们的方法优于现有的ICA方法，包括SOBI算法。此外，我们研究了所提出的方法的渐近行为。
Independent component analysis (ICA) is a blind source separation method to recover source signals of interest from their mixtures. Most existing ICA procedures assume independent sampling. Second-order-statistics-based source separation methods have been developed based on parametric time series models for the mixtures from the autocorrelated sources. However, the second-order-statistics-based methods cannot separate the sources accurately when the sources have temporal autocorrelations with mixed spectra. To address this issue, we propose a new ICA method by estimating spectral density functions and line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated by maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through simulation experiments and an EEG data application. The numerical results indicate that our approach outperforms existing ICA methods, including SOBI algorithms. In addition, we investigate the asymptotic behavior of the proposed method.
