Blind Source Separation and Blind Mixture Identification Methods

Abstract

Blind source separation (BSS) is a generic signal processing problem. BSS methods aim to estimate a set of unknown source signals, by using a set of available signals that are mixtures of the source signals to be restored, with limited or no knowledge of the mixing transform (i.e., the transform of source signals that yields their mixtures). BSS methods were introduced in the 1980s and then quickly expanded. Various books provide a detailed description of BSS methods, or at least of some classes of such methods defined hereafter, such as independent component analysis, sparse component analysis, and nonnegative matrix factorization. Moreover, the BSS problem, focused on signal restoration, is closely linked to the estimation of the mixing transform, and thus to the problem often referred to as blind mixture identification (BMI). In this article, we overview the fields of BSS and BMI. We first define in more detail the considered goal (Section 1) and conditions of investigation (Section 2), and then we introduce the major classes of methods that make it possible to solve the considered problems. The presentation of BSS/BMI methods themselves and of typical applications is given in successive sections (Sections 3–7), where we progress from standard to more advanced configurations, in terms of properties of source signals and class of mixing transform.