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.
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| 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. | ||||||||||||||
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| 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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