Candès, Emmanuel and Romberg, Justin (2006) Encoding the ℓ_p ball from limited measurements. In: DCC 2006: Data Compression Conference, Proceedings. IEEE Data Compression Conference. IEEE , Los Alamitos, CA, pp. 33-42. ISBN 0-7695-2545-8. https://resolver.caltech.edu/CaltechAUTHORS:20110225-083247917
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Abstract
We address the problem of encoding signals which are sparse, i.e. signals that are concentrated on a set of small support. Mathematically, such signals are modeled as elements in the ℓ_p ball for some p ≤ 1. We describe a strategy for encoding elements of the ℓ_p ball which is universal in that 1) the encoding procedure is completely generic, and does not depend on p (the sparsity of the signal), and 2) it achieves near-optimal minimax performance simultaneously for all p < 1. What makes our coding procedure unique is that it requires only a limited number of nonadaptive measurements of the underlying sparse signal; we show that near-optimal performance can be obtained with a number of measurements that is roughly proportional to the number of bits used by the encoder. We end by briefly discussing these results in the context of image compression.
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 2006 IEEE. Issue Date: 28-30 March 2006. Date of Current Version: 10 April 2006. | |||||||||
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| Series Name: | IEEE Data Compression Conference | |||||||||
| DOI: | 10.1109/DCC.2006.86 | |||||||||
| Record Number: | CaltechAUTHORS:20110225-083247917 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20110225-083247917 | |||||||||
| Official Citation: | Candes, E.; Romberg, J.; , "Encoding the ℓp ball from limited measurements," Data Compression Conference, 2006. DCC 2006. Proceedings , vol., no., pp. 33- 42, 28-30 March 2006 doi: 10.1109/DCC.2006.86 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1607238&isnumber=33750 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 22507 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 25 Feb 2011 17:12 | |||||||||
| Last Modified: | 09 Nov 2021 16:05 |
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