License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2012.230
URN: urn:nbn:de:0030-drops-34011
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3401/
Go to the corresponding LIPIcs Volume Portal

Ngo, Hung Q. ; Porat, Ely ; Rudra, Atri

Efficiently Decodable Compressed Sensing by List-Recoverable Codes and Recursion

pdf-format:
17.pdf (0.6 MB)

Abstract

We present two recursive techniques to construct compressed sensing schemes that can be "decoded" in sub-linear time. The first technique is based on the well studied code composition method called code concatenation where the "outer" code has strong list recoverability properties. This technique uses only one level of recursion and critically uses the power of list recovery. The second recursive technique is conceptually similar, and has multiple recursion levels. The following compressed sensing results are obtained using these techniques:

- Strongly explicit efficiently decodable l_1/l_1 compressed sensing matrices: We present a strongly explicit ("for all") compressed sensing measurement matrix with O(d^2log^2 n) measurements that can output near-optimal d-sparse approximations in time poly(d log n).
- Near-optimal efficiently decodable l_1/l_1 compressed sensing matrices for non-negative signals: We present two randomized constructions of ("for all") compressed sensing matrices with near optimal number of measurements: O(d log n loglog_d n) and O_{m,s}(d^{1+1/s} log n (log^(m) n)^s), respectively, for any integer parameters s,m>=1. Both of these constructions can output near optimal d-sparse approximations for non-negative signals in time poly(d log n).

To the best of our knowledge, none of the results are dominated by existing results in the literature.

BibTeX - Entry

@InProceedings{ngo_et_al:LIPIcs:2012:3401,
  author =	{Hung Q. Ngo and Ely Porat and Atri Rudra},
  title =	{{Efficiently Decodable Compressed Sensing by List-Recoverable Codes and Recursion}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{230--241},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{Christoph D{\"u}rr and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3401},
  URN =		{urn:nbn:de:0030-drops-34011},
  doi =		{10.4230/LIPIcs.STACS.2012.230},
  annote =	{Keywords: Compressed Sensing, Sub-Linear Time Decoding, List-Recoverable Codes}
}

Keywords: Compressed Sensing, Sub-Linear Time Decoding, List-Recoverable Codes
Collection: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Issue Date: 2012
Date of publication: 24.02.2012

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI