Gabor fusion frames generated by difference sets

Irena Bojarovska; Victoria Paternostro

doi:10.1117/12.2186394

24 August 2015 Gabor fusion frames generated by difference sets

Irena Bojarovska, Victoria Paternostro

Proceedings Volume 9597, Wavelets and Sparsity XVI; 95970D (2015) https://doi.org/10.1117/12.2186394
Event: SPIE Optical Engineering + Applications, 2015, San Diego, California, United States

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.

Citation Download Citation

Irena Bojarovska and Victoria Paternostro "Gabor fusion frames generated by difference sets", Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970D (24 August 2015); https://doi.org/10.1117/12.2186394

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