On the Search for Tight Frames of Low Coherence

Abstract

We introduce a projective Riesz s-kernel for the unit sphere S d−1 and investigate properties of N -point energy minimizing configurations for such a kernel. We show that these configurations, for s and N sufficiently large, form frames that are well-separated (have low coherence) and are nearly tight. Our results suggest an algorithm for computing well-separated tight frames which is illustrated with numerical examples.