Tight p-fusion frames

Details Tight p-fusion frames Tight p-fusion frames

2012-01-09

arxiv.org/abs/1201.1798v1

Mathematics

Numerical Analysis

Scientific paper

Fusion frames enable signal decompositions into weighted linear subspace components. We introduce tight p-fusion frames, a sharpening of the notion of tight fusion frames. This notion is closely related to the classical notions of designs and cubature formulas in Grassmann spaces and is analyzed with methods from harmonic analysis in the Grassmannians. We show that, when p components are lost, equidimensional tight p-fusion frames that are also cubature formulas of strength 4 allow for reconstruction of a finite list of potential signals, one of which is the correct one. We also verify a simplex bound for subspaces of arbitrary dimensions, characterize the case of equality in this bound by an equiangular property, and derive an upper bound on the maximal number of equiangular subspaces. We define the p-fusion frame potential, discuss bounds for its value, and connections to the simplex bound and to p-tight fusion frames.

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