Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation

TL;DR

This paper introduces differential fixed-point algorithms for underdetermined blind source separation, extending FastICA and C-FICA methods to improve robustness against noise in instantaneous and convolutive mixtures.

Contribution

It proposes novel differential extensions of FastICA and C-FICA for underdetermined BSS, enhancing robustness and applicability to nonstationary sources.

Findings

Differential algorithms outperform standard methods in noisy environments.

Extensions work for both instantaneous and convolutive mixtures.

Algorithms maintain the attractive features of original FastICA and C-FICA.

Abstract

This paper concerns underdetermined linear instantaneous and convolutive blind source separation (BSS), i.e., the case when the number of observed mixed signals is lower than the number of sources.We propose partial BSS methods, which separate supposedly nonstationary sources of interest (while keeping residual components for the other, supposedly stationary, "noise" sources). These methods are based on the general differential BSS concept that we introduced before. In the instantaneous case, the approach proposed in this paper consists of a differential extension of the FastICA method (which does not apply to underdetermined mixtures). In the convolutive case, we extend our recent time-domain fast fixed-point C-FICA algorithm to underdetermined mixtures. Both proposed approaches thus keep the attractive features of the FastICA and C-FICA methods. Our approaches are based on differential sphering processes, followed by the optimization of the differential nonnormalized kurtosis that we introduce in this paper. Experimental tests show that these differential algorithms are much more robust to noise sources than the standard FastICA and C-FICA algorithms.