Estimación de la matriz de mezclas en separación ciega de fuentes indeterminada con un número arbitrario de fuentes

Abstract

Blind source separation consists on estimating n source signals from m measurements generated through an unknown mixing process of the sources. In the underdetermined case where we have more sources than measurements, we divide the problem into two stages: estimation of the mixing matrix and inversion of the linear problem. This paper deals with the first stage. It is well known that when the sparsity of the sources premise is true, measurements tend to align with the columns of the mixing matrix, so the problem can be formulated as estimating the peaks of multidimensional probability density functions (PDF). In this paper we analyze two different techniques to estimate this peaks: one is to convert the multidimensional PDF into the power spectral density (PSD) of multiple complex sinusoidal signals and use different multidimensional espectral estimation techniques to detect the peaks. The other is to convert the (m − 1)- multidimensional PDF to m − 1 unidimensional projections and estimate the peaks of these.