Estimating Sparse Sources from Data Mixtures using Maxima in Phase Space Plots

TL;DR

This paper introduces a phase space analysis method for Sparse Component Analysis in Blind Source Separation, estimating sources from data mixtures by identifying maxima in phase plots, with tests on simulated and real ECG data.

Contribution

The paper presents a novel phase space analysis approach for SCA that estimates sources from maxima in phase plots, offering a new technique compared to existing methods.

Findings

Performance comparable to PCA and FastICA on clean data

PCA more robust than the proposed method at high noise levels

Method fails when sources have coincident peaks

Abstract

In Blind Source Separation (BSS), one estimates sources from data mixtures where the mixing coefficients are unknown. In the particular case of Sparse Component Analysis (SCA), each underlying source exists for only a finite amount of time when other sources are negligible. In this paper, one approach to SCA is presented where the data are represented using phase space analysis and one estimates the main source from the maximum in the phase plot. Deflation is used to estimate the other sources. The proposed method is tested on simulated data and experimental ECG data taken from an expectant mother. It is shown that, in most cases, the performance of the proposed method is comparable to that of Principal Component Analysis (PCA) and FastICA for clean data. In the case of noisy data, PCA is found to be more robust for higher noise levels. For situations where the sources have coincident peaks, the method breaks down as expected, as the maximum in the phase plot does not correspond to an individual source.