Estimation of the mixing matrix for underdetermined blind source separation using spectral estimation techniques

Blind source separation is concerned with estimating n source signals from m measurements that are generated through an unknown mixing process. In the underdetermined linear case, where the number of measurements is smaller than the number of sources, the solution can be obtained in three stages: represent the signals in a sparse domain, estimate the mixing matrix, and evaluate the sources using the available previous knowledge. This paper deals with the second stage, that can be formulated as to find the peaks location of a probability density function (PDF). It is shown that when the premise of sparse signals is satisfied, the densities resemble the power spectral density (PSD) of sinusoids in noise. The analogy between a PDF and a PSD allows us to apply spectral estimation techniques to determine the mixing matrix. According to the shape of the PDF's, parametric methods for line spectra have been applied.