Differential source separation: Concept and application to a criterion based on differential normalized kurtosis

This paper concerns the underdetermined case of the blind source separation problem, i.e. the situation when the number of observed mixed signals is lower than the number of sources. The general concept that we propose in this case consists of a differential source separation approach, which uses optimization criteria based on differential parameters, so as to make some sources invisible in these criteria and to perform an exact separation of the other sources only. We illustrate this partial source separation concept on a new criterion based on the "differential normalized kurtosis" that we introduce to this end. We then validate the performance of this criterion by means of experimental tests.