International Conference on Multivariate Approximation
September 24-27, 2011

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Optimal fusion frames

Martin Ehler
, Christine Bachoc
Fusion frames enable signal decompositions into weighted linear subspace components and provide efficient reconstruction formulas. We introduce the p-fusion frame potential and verify that its minimizers suppress correlated noise most efficiently. In fact, cubature formulas for Grassmann spaces are minimizers, and, if p goes to infinity, our estimates of the p-fusion frame potential generalize the simplex bound known in coding theory. If the simplex bound is matched, then the subspaces must be equiangular, and we derive an upper bound on the number of equiangular subspaces. The above concepts are also carried over into a probabilistic setting.