On the Search for Tight Frames of Low Coherence

Abstract

We introduce a projective Riesz $s$-kernel for the unit sphere ${\mathbb{S}}^{d-1}$ 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.

26 pages