Scheduled System Maintenance:
Some services will be unavailable Sunday, March 29th through Monday, March 30th. We apologize for the inconvenience.
By Topic

Simple deterministically constructible RIP matrices with sublinear fourier sampling requirements

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)
Iwen, M.A. ; Inst. for Math. & its Applic. (IMA), Univ. of Minnesota, Minneapolis, MN

We present a deterministic number theoretic construction for matrices with the restricted isometry property (RIP). Furthermore, we show that the number theoretic properties of our RIP matrices allow their products with discrete Fourier transform (DFT) matrices to be well approximated via a few highly sparse matrix multiplications. Hence, our RIP matrices may be approximately multiplied by the DFT of any input vector in sublinear-time by reading only a small fraction of its entries. As a consequence, we obtain small deterministic sample sets which are guaranteed to allow the recovery of near-optimal sparse Fourier representations for all periodic functions having an integrable second derivative over a single period. Explicit bounds are provided for the sizes of our RIP matrices, the sizes of their associated sublinear Fourier sampling sets, and the errors incurred by quickly approximating their products with DFT matrices. The Fourier sampling requirements obtained herein improve on previous deterministic Fourier sampling results in [1], [2].

Published in:

Information Sciences and Systems, 2009. CISS 2009. 43rd Annual Conference on

Date of Conference:

18-20 March 2009