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Frames from generalized group fourier transforms and SL_2(F_q)

Thill, Matthew and Muthukumar, Vidya and Hassibi, Babak (2014) Frames from generalized group fourier transforms and SL_2(F_q). In: 2014 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE , Piscataway, NJ, pp. 4923-4927. ISBN 978-1-4799-2892-7. https://resolver.caltech.edu/CaltechAUTHORS:20150106-132022513

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Abstract

We explore the problem of deterministically constructing frames and matrices with low coherence, which arises in areas such as compressive sensing, spherical codes, and MIMO communications. In particular, we present a generalization of the familiar harmonic frame by selecting a subset of rows of the generalized discrete Fourier transform matrix over finite groups. We apply our methods to the group SL_2(F_q) and show how to produce frames with remarkably low coherence, for which we provide upper bounds.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ICASSP.2014.6854538 DOIArticle
ORCID:
AuthorORCID
Thill, Matthew0000-0003-0885-6260
Additional Information:© 2014 IEEE. This work was supported in part by the National Science Foundation under grants CCF-0729203, CNS-0932428 and CCF-1018927, by the Office of Naval Research under the MURI grant N00014-08-1-0747, and by Caltech’s Lee Center for Advanced Networking. The first author was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.
Funders:
Funding AgencyGrant Number
NSFCCF-0729203
NSFCNS-0932428
NSFCCF-1018927
Office of Naval Research (ONR)N00014-08-1-0747
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
National Defense Science and Engineering Graduate (NDSEG) FellowshipUNSPECIFIED
Subject Keywords:Coherence; frame; unit norm tight frame; group representation; special linear group; spherical codes; compressive sensing
Record Number:CaltechAUTHORS:20150106-132022513
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150106-132022513
Official Citation:Thill, M.; Muthukumar, V.; Hassibi, B., "Frames from generalized group fourier transforms and SL2(Fq)," Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on , vol., no., pp.4923,4927, 4-9 May 2014 doi: 10.1109/ICASSP.2014.6854538 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6854538&isnumber=6853544
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53214
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Jan 2015 17:20
Last Modified:27 Aug 2020 20:07

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