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arXiv · 1507.01829

Gabor fusion frames generated by difference sets

Irena Bojarovska·Victoria Paternostro
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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 was shown in \cite{xia2005achieving} 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 $N^2$ 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, Victoria Paternostro. 2015-07-07. Gabor fusion frames generated by difference sets. https://doi.org/10.1117/12.2186394

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