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Proceedings Paper

Gabor fusion frames generated by difference sets
Author(s): Irena Bojarovska; Victoria Paternostro
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Paper 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.

Paper Details

Date Published: 24 August 2015
PDF: 14 pages
Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970D (24 August 2015); doi: 10.1117/12.2186394
Show Author Affiliations
Irena Bojarovska, Technische Univ. Berlin (Germany)
Victoria Paternostro, Univ. de Buenos Aires (Argentina)
IMAS-CONICET (Argentina)


Published in SPIE Proceedings Vol. 9597:
Wavelets and Sparsity XVI
Manos Papadakis; Vivek K. Goyal; Dimitri Van De Ville, Editor(s)

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