CaltechAUTHORS
  A Caltech Library Service

The value of redundant measurement in compressed sensing

Kostina, Victoria and Duarte, Marco F. and Jafarpour, Sina and Calderbank, Robert (2011) The value of redundant measurement in compressed sensing. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). International Conference on Acoustics Speech and Signal Processing ICASSP. IEEE , Piscataway, NJ, pp. 3656-3659. ISBN 978-1-4577-0538-0. https://resolver.caltech.edu/CaltechAUTHORS:20140910-103127300

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20140910-103127300

Abstract

The aim of compressed sensing is to recover attributes of sparse signals using very few measurements. Given an overall bit budget for quantization, this paper demonstrates that there is value to redundant measurement. The measurement matrices considered here are required to have the property that signal recovery is still possible even after dropping certain subsets of D measurements. It introduces the concept of a measurement matrix that is weakly democratic in the sense that the amount of information about the signal carried by each of the designated D-subsets is the same. Examples of deterministic measurement matrices that are weakly democratic are constructed by exponentiating codewords from the binary second order Reed Muller code. The value in rejecting D measurements that are on average larger, is to be able to provide a finer grid for vector quantization of the remaining measurements, even after discounting the original budget by the bits used to identify the reject set. Simulation results demonstrate that redundancy improves recovery SNR, sometimes by a wide margin. Optimum performance occurs when a significant fraction of measurements are rejected.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5947143PublisherArticle
http://dx.doi.org/10.1109/ICASSP.2011.5947143DOIArticle
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2011 IEEE. This work was supported in part by NSF under grant DMS-0914892, by ONR under grant N00014-08-1-1110, and by AFOSR under grants FA9550-09-1-0643 and FA9550-09-1-0551. V. Kostina was supported in part by the Natural Sciences and Engineering Research Council of Canada. M. F. Duarte was supported in part by NSF Supplemental Funding DMS-0439872 to UCLA-IPAM,P.I.
Funders:
Funding AgencyGrant Number
NSFDMS-0914892
Office of Naval Research (ONR)N00014-08-1-1110
Air Force Office of Scientific Research (AFOSR)FA9550-09-1-0643
Air Force Office of Scientific Research (AFOSR)FA9550-09-1-0551
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
NSFDMS-0439872
Subject Keywords:Compressed sensing, quantization, democracy, saturation
Series Name:International Conference on Acoustics Speech and Signal Processing ICASSP
Record Number:CaltechAUTHORS:20140910-103127300
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140910-103127300
Official Citation:Kostina, V.; Duarte, M.F.; Jafarpour, Sina; Calderbank, R., "The value of redundant measurement in compressed sensing," Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on , vol., no., pp.3656,3659, 22-27 May 2011 doi: 10.1109/ICASSP.2011.5947143
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49533
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:09 Mar 2020 14:56
Last Modified:03 Oct 2019 07:14

Repository Staff Only: item control page