Blind source separation with noisy sources

A new method of source separation with noisy observations is proposed in the case of two sensors. Each observation contains a mixture of two signals with noise. The objective is to estimate the frequency spectra of the linear filters that combine the two signals in the data stream. The main characteristic of the method is to take into account additive noises. No hypotheses on their probability densities are made. We derive for that an original objective function, based on nonlinear functions of the observations. Specific properties of these functions, chosen as exponential functions, and the hypothesis of independent sources lead to a direct solution for the estimation of the filters. An analytic solution may be computed from it, using only the data. The convergence speed of the method and its robustness against non gaussian noise are illustrated in the paper with simulation results.