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A second-order differential approach for underdetermined convolutive source separation

This paper concerns the underdetermined case of the convolutive source separation problem, i.e. the situation when the number of observed convolutively mixed signals is lower than the number of sources. We propose a criterion and associated algorithm which, unlike classical approaches, make it possible to perform the separation of a subset of these sources by exploiting their assumed non-stationarity properties. This approach uses the second-order statistics of the signals and adapts the filters of a direct separating system so as to cancel the "differential cross-correlation" of signals derived by this system. This new method is related to the general differential source separation concept that we proposed. Its effectiveness is shown by means of numerical tests.