The Minimum Support Criterion for Blind Signal Extraction: A Limiting Case of the Strengthened Young’s Inequality

Abstract

In this paper, we address the problem of the blind extraction of a subset of “interesting” independent signals from a linear mixture. We present a novel criterion for the extraction of the sources whose density has the minimum support measure. By extending the definition of the Renyi’s entropies to include the zero-order case, this criterion can be regarded as part of a more general entropy minimization principle. It is known that Renyi’s entropies provide contrast functions for the blind extraction of independent and identically distributed sources under an ∞-norm constraint on the global transfer system. The proposed approach gives sharper lower-bounds for the zero-order Renyi’s entropy case and, contrary to the existing results, it allows the extraction even when the sources are non identically distributed. Another interesting feature is that it is robust to the presence of certain kinds of additive noise and outliers in the observations.