Nonparametric Independent Component Analysis for the Sources with Mixed Spectra

TL;DR

This paper introduces a nonparametric ICA method that estimates spectral densities to better separate sources with mixed spectra, outperforming existing methods like SOBI in simulations and EEG data.

Contribution

The paper proposes a novel nonparametric ICA technique using spectral density estimation with cubic splines and indicator functions, addressing limitations of autocorrelation-based methods.

Findings

Outperforms SOBI algorithms in simulations

Effective in separating sources with mixed spectra

Demonstrated success on EEG data

Abstract

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.