A robust geometrical method for blind separation of noisy mixtures of non-negatives sources

Abstract

Recently, we proposed an effective geometrical method for separating linear instantaneous mixtures of non-negative sources, termed Simplicial Cone Shrinking Algorithm for Unmixing Non-negative Sources (SCSA-UNS). The latter method operates in noiseless case, and estimates the mixing matrix and the sources by finding the minimum aperture simplicial cone, containing the scatter plot of mixed data. In this paper, we propose an extension of SCSA-UNS, to tackle the noisy mixtures, in the case where the sparsity degrees of the sources are known a priori. The idea is to progressively eliminate, the noisy mixed data points which are likely to significantly modify the scatter plot of noiseless mixed data and to lead to a bad estimation of the mixing matrix and the sources. Simulations on synthetic data show the effectiveness of the proposed method.