Robust Underdetermined Algorithm Using Heuristic-Based Gaussian Mixture Model for Blind Source Separation

Abstract

Blind source separation (BSS) involves recovering unobserved source signals from several mixed observations, typically obtained at the output of a set of sensors. Each sensor receives a different combination of the source signals. The adjective “blind” emphasizes the fact that: first, the source signals are not observed; and next, no information is available about the mixture. The assumption is often held physically that the source signals are mutually independent. Recently, BSS in signal processing has received considerable attention from researchers, due to its numerous promising applications in the areas of biomedical signal processing, digital communications and speech signal, sonar, image processing, and monitoring (Cichocki & Unbehauen, 1996), (Tangdiongga et al, 2001), (Yilmaz & Rickard, 2004), (Herault & Juten, 1986). A number of blind separation algorithms have been proposed based on different separation models. These algorithms play increasingly important roles in many applications. Since the pioneering work of Jutten and Herault (Herault & Juten, 1986), a variety of algorithms have been proposed for BSS. In general, the existing algorithms can be divided into five major categories: neural network-based algorithms (Cichocki & Unbehauen, 1996), (Zhang & Kassam, 2004), density model-based algorithms (Amari et al, 1997), (Lee et al, 1999a), algebraic algorithms (Belouchrani et al, 1997), (Li & Wang, 2002), information-theoretic algorithms (Pajunen, 1998), (Pham & Vrins, 2005) and space-based algorithms (Yilmaz & Rickard, 2004), (Lee et al, 1999b). A source signal with sparse representation means that at most one value of the signal isn’t zero at an instant, making the vector of sensor signals (mixtures) equivalent to some mixing vector. Therefore, the sparse-based BSS problem could be solved by searching for mixing vectors; moreover, recovering source signals. Like the mixtures with sparse representation, each base vectors of the unknown mixing matrix will be displayed on a 2-D plane coordinate as a directional line when two sensors are used. The sparse representation is first introduced in underdetermined BSS by Lee et al. (Lee et al, 1999b). After its introduction, several related methods have been proposed continuously for solving underdetermined BSS