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

Compressed Sensing With Nonlinear Observations and Related Nonlinear Optimization Problems

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

1 Author(s)
Blumensath, T. ; ISVR Signal Process. & Control Group, Univ. of Southampton, Southampton, UK

Nonconvex constraints are valuable regularizers in many optimization problems. In particular, sparsity constraints have had a significant impact on sampling theory, where they are used in compressed sensing and allow structured signals to be sampled far below the rate traditionally prescribed. Nearly, all of the theory developed for compressed sensing signal recovery assumes that samples are taken using linear measurements. In this paper, we instead address the compressed sensing recovery problem in a setting where the observations are nonlinear. We show that, under conditions similar to those required in the linear setting, the iterative hard thresholding algorithm can be used to accurately recover sparse or structured signals from few nonlinear observations. Similar ideas can also be developed in a more general nonlinear optimization framework. In the second part of this paper, we therefore present related result that shows how this can be done under sparsity and union of subspaces constraints, whenever a generalization of the restricted isometry property traditionally imposed on the compressed sensing system holds.

Published in:

Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 6 )

Date of Publication:

June 2013

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.