Nonparametric Independent Component Analysis for the Sources with Mixed Spectra
This addresses a specific bottleneck in blind source separation for signals like EEG data, but it is incremental as it builds on existing ICA frameworks.
The paper tackles the problem of separating autocorrelated sources with mixed spectra in independent component analysis (ICA), proposing a method that estimates spectral densities and line spectra using cubic splines and indicator functions. The results show it outperforms existing ICA methods, including SOBI algorithms, in simulations and an EEG application.
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.