A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources

In this paper, we propose a new blind source separation (BSS) method called TIme-Frequency Ratio Of Mixtures (TIFROM) which uses time-frequency (TF) information to cancel source signal contributions from a set of linear instantaneous mixtures of these sources. Unlike previously reported TF BSS methods, the proposed approach only requires slight differences in the TF distributions of the considered signals: it mainly requests the sources to be cancelled to be “visible”, i.e. to occur alone in a tiny area of the TF plane, while they may overlap in all the remainder of this plane. By using TF ratios of mixed signals, it automatically determines these single-source TF areas and identifies the corresponding parts of the mixing matrix. This approach sets no conditions on the stationarity, independence or non-Gaussianity of the sources, unlike classical independent component analysis methods. It achieves complete or partial BSS, depending on the numbers N and P of sources and observations and on the number of visible sources. It is therefore of interest for underdetermined mixtures (i.e. N>P), which cannot be processed with classical methods. Detailed results concerning mixtures of speech and music signals are presented and show that this approach yields very good performance.