Exploring Bounded Component Analysis Using an $\ell_\infty$ Norm Criterion

TL;DR

This paper introduces a new criterion based on the $\ell_ extinfty$ norm for blind source separation of antisparse bounded signals, demonstrating its effectiveness through theoretical analysis and simulations.

Contribution

It proposes a novel $\ell_ extinfty$-norm based criterion and optimization method for separating bounded sources, including correlated and antisparse signals.

Findings

The $\ell_ extinfty$ norm is effective as a contrast function for antisparse sources.

The proposed method outperforms existing algorithms in simulations.

The approach works for both independent and correlated bounded sources.

Abstract

In this paper we propose a new criterion for the Blind Source Separation (BSS) of antisparse bounded sources, based on the sum of the $\ell_\infty$-norm of the sources. Based on the observation that the mixing process of bounded sources with any mixing matrix with unitary Frobenius norm will increase the $\ell_\infty$-norm of the sources, unless it is the identity matrix, the minimization of the sum of the $\ell_\infty$-norm of the sources can be used for the estimation of a separation matrix. To that, a Principle Component Analysis technique followed by a Givens Rotations based optimization method can be used for the separation of independent bounded sources. Also, the Givens Rotations based optimization method can be used for the separation of correlated bounded sources mixed by a rotation matrix. We theoretically analyze the proposed criterion and assess its performance through numerical simulations involving three distinct types of bounded signals. Our theoretical and experimental findings underscore the efficacy of the $\ell_\infty$ norm as a suitable contrast function for antisparse bounded sources, showcasing its superior performance relative to a state-of-the-art algorithm.