Cart (Loading....) | Create Account
Close category search window
 

Information-Theoretic Limits on Sparse Signal Recovery: Dense versus Sparse Measurement Matrices

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Wei Wang ; Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA, USA ; Wainwright, M.J. ; Ramchandran, K.

We study the information-theoretic limits of exactly recovering the support set of a sparse signal, using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of observations n, the ambient signal dimension p, and the signal sparsity k are all allowed to tend to infinity in a general manner. This paper makes two novel contributions. First, we provide sharper necessary conditions for exact support recovery using general (including non-Gaussian) dense measurement matrices. Combined with previously known sufficient conditions, this result yields sharp characterizations of when the optimal decoder can recover a signal for various scalings of the signal sparsity k and sample size n, including the important special case of linear sparsity (k = ¿(p)) using a linear scaling of observations (n = ¿(p)). Our second contribution is to prove necessary conditions on the number of observations n required for asymptotically reliable recovery using a class of ¿-sparsified measurement matrices, where the measurement sparsity parameter ¿(n, p, k) ¿ (0,1] corresponds to the fraction of nonzero entries per row. Our analysis allows general scaling of the quadruplet (n, p, k, ¿) , and reveals three different regimes, corresponding to whether measurement sparsity has no asymptotic effect, a minor effect, or a dramatic effect on the information-theoretic limits of the subset recovery problem.

Published in:

Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 6 )

Date of Publication:

June 2010

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.