24 August 2015 Gabor fusion frames generated by difference sets
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Abstract
Collections of time- and frequency-shifts of suitably chosen generators (Alltop or random vectors) proved successful for many applications in sparse recovery and related fields. It is known1 that taking a characteristic function of a difference set as a generator, and considering only the frequency shifts, gives an equaingular tight frame for the subspace they span. In this paper, we investigate the system of all N2 time- and frequency-shifts of a difference set in dimension N via the mutual coherence, and compare numerically its sparse recovery effectiveness with Alltop and random generators. We further view this Gabor system as a fusion frame, show that it is optimally sparse, and moreover an equidistant tight fusion frame, i.e. it is an optimal Grassmannian packing.
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Irena Bojarovska, Irena Bojarovska, Victoria Paternostro, Victoria Paternostro, } "Gabor fusion frames generated by difference sets", Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970D (24 August 2015); doi: 10.1117/12.2186394; https://doi.org/10.1117/12.2186394
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