Gabor fusion frames generated by difference sets

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...

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Autores principales: Bojarovska, I., Paternostro, V., Goyal V.K., Van De Ville D., Van De Ville, Papadakis M., The Society of Photo-Optical Instrumentation Engineers (SPIE)
Formato: CONF
Materias:
Fusion frames
Gabor systems
Mutual coherence
Time-frequency analysis
Welch bound
Optical engineering
Time frequency analysis
Welch bounds
Frequency shift keying
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0277786X_v9597_n_p_Bojarovska
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0277786X_v9597_n_p_Bojarovska
record_format dspace
spelling todo:paper_0277786X_v9597_n_p_Bojarovska2023-10-03T15:16:48Z Gabor fusion frames generated by difference sets Bojarovska, I. Paternostro, V. Goyal V.K. Van De Ville D. Van De Ville Papadakis M. Van De Ville D. Papadakis M. Goyal V.K. Van De Ville The Society of Photo-Optical Instrumentation Engineers (SPIE) Fusion frames Gabor systems Mutual coherence Time-frequency analysis Welch bound Optical engineering Fusion frames Gabor systems Mutual coherence Time frequency analysis Welch bounds Frequency shift keying 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. © 2015 SPIE. Fil:Paternostro, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. CONF info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0277786X_v9597_n_p_Bojarovska
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fusion frames
Gabor systems
Mutual coherence
Time-frequency analysis
Welch bound
Optical engineering
Fusion frames
Gabor systems
Mutual coherence
Time frequency analysis
Welch bounds
Frequency shift keying
spellingShingle Fusion frames
Gabor systems
Mutual coherence
Time-frequency analysis
Welch bound
Optical engineering
Fusion frames
Gabor systems
Mutual coherence
Time frequency analysis
Welch bounds
Frequency shift keying
Bojarovska, I.
Paternostro, V.
Goyal V.K.
Van De Ville D.
Van De Ville
Papadakis M.
Van De Ville D.
Papadakis M.
Goyal V.K.
Van De Ville
The Society of Photo-Optical Instrumentation Engineers (SPIE)
Gabor fusion frames generated by difference sets
topic_facet Fusion frames
Gabor systems
Mutual coherence
Time-frequency analysis
Welch bound
Optical engineering
Fusion frames
Gabor systems
Mutual coherence
Time frequency analysis
Welch bounds
Frequency shift keying
description 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. © 2015 SPIE.
format CONF
author Bojarovska, I.
Paternostro, V.
Goyal V.K.
Van De Ville D.
Van De Ville
Papadakis M.
Van De Ville D.
Papadakis M.
Goyal V.K.
Van De Ville
The Society of Photo-Optical Instrumentation Engineers (SPIE)
author_facet Bojarovska, I.
Paternostro, V.
Goyal V.K.
Van De Ville D.
Van De Ville
Papadakis M.
Van De Ville D.
Papadakis M.
Goyal V.K.
Van De Ville
The Society of Photo-Optical Instrumentation Engineers (SPIE)
author_sort Bojarovska, I.
title Gabor fusion frames generated by difference sets
title_short Gabor fusion frames generated by difference sets
title_full Gabor fusion frames generated by difference sets
title_fullStr Gabor fusion frames generated by difference sets
title_full_unstemmed Gabor fusion frames generated by difference sets
title_sort gabor fusion frames generated by difference sets
url http://hdl.handle.net/20.500.12110/paper_0277786X_v9597_n_p_Bojarovska
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