On the search for tight frames of low coherence
We introduce a projective Riesz s-kernel for the unit sphere S^ d-1 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.
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.
Abstract
We introduce a projective Riesz s-kernel for the unit sphere 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.
Springer
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