Blind Source Separation of Underdetermined Mixtures Based on Local Mean Decomposition and Conjugate Gradient Algorithm

Abstract

Most of the existing underdetermined blind source separation (BSS) approaches assume that the source signals are strictly or partially sparse. This paper, however, presents a new BSS method in underdetermined mixing situation for non- sparse signals. The proposed method first introduces the local mean decomposition algorithm into the BSS problem to rebuild some extra mixing signals. Such signals are then combined with the initial mixtures such that the underdetermined BSS problem is transformed to a determined one and the difficulty of the deficiency of the mixtures is overcome. For the rebuilt mixtures and the newly formed determined BSS problem, the minimum mutual information principle is employed as the BSS cost function. A conjugate gradient learning algorithm is then derived for training the separating matrix. In each update step of the algorithm, the term of score function is estimated by a kernel function estimation algorithm. The simulation results have demonstrated the efficacy of the proposed underdetermined BSS method.  Index Terms—Blind source separation, underdetermined model, local mean decomposition, conjugate gradient