Special Seminar in Applied Mathematics
Tight p-fusion frames for signal decomposition
We first derive an upper bound on the maximal number of mutually equiangular subspaces. We circumvent this limitation for robustness against erasures by extending the concept of fusion frames and by changing the measure of robustness. Our main contribution is the introduction of the notion of tight p-fusion frames, a sharpening of the notion of tight fusion frames, that is closely related to the classical notions of designs and cubature formulas in Grassmann spaces. We analyze tight p-fusion frames with methods from harmonic analysis in the Grassmannians.
Finally, we verify that tight p-fusion frames are robust against up to p subspace erasures.
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