A Recursive Least-squares Extension of the Natural Gradient Algorithm for Blind Signal Separation of Audio Mixtures

Blind Signal Separation (BSS) refers to the operation of recovering a set of sources that are as independent as possible from another set of observed linear or non-linear mixtures. The term blind indicates that this operation is done without knowing the mixing coefficients. Although this problem is more difficult than the classical filtering problem, a solution is still feasible provided that some information about the original independent components is provided. Major attention in the literature has been focused on different criteria to be used as objective functions for BSS. However, most of the existing on-line methods can be categorized as using a stochastic gradient. The need for second-order based algorithms for BSS can be easily revealed, as the fast convergence rate of the Recursive-Least-Squares (RLS) based algorithms can be advantageous for many applications. Among the many existing objective functions for Blind Signal Separation, Maximum Likelihood and Negentropy stand as strong criteria which are well justified, as they minimize the mutual information between the original independent components [1],[2]. Maximum likelihood proved especially suitable for heavy tailed distribution signals, such as audio data [3].