NDLI: Toeplitz-Structured Compressed Sensing Matrices

Content Provider	IEEE Xplore Digital Library
Author	Bajwa, Waheed U. Haupt, Jarvis D. Raz, Gil M. Wright, Stephen J. Nowak, Robert D.
Copyright Year	2007
Description	Author affiliation: GMR Research and Technology, Concord, MA 01742-3819. E-mail: raz@gmrtech.com (Raz, Gil M.) \|\| Department of Electrical and Computer Engineering, University of Wisconsin-Madison. E-mail: jdhaupt@wisc.edu (Haupt, Jarvis D.) \|\| Department of Electrical and Computer Engineering, University of Wisconsin-Madison. E-mail: nowak@engr.wisc.edu (Nowak, Robert D.) \|\| Department of Electrical and Computer Engineering, University of Wisconsin-Madison. E-mail: bajwa@cae.wisc.edu (Bajwa, Waheed U.) \|\| Department of Computer Sciences, University of Wisconsin-Madison. E-mail: swright@cs.wisc.edu (Wright, Stephen J.)
Abstract	The problem of recovering a sparse signal x Rn from a relatively small number of its observations of the form y = Ax Rk, where A is a known matrix and k « n, has recently received a lot of attention under the rubric of compressed sensing (CS) and has applications in many areas of signal processing such as data cmpression, image processing, dimensionality reduction, etc. Recent work has established that if A is a random matrix with entries drawn independently from certain probability distributions then exact recovery of x from these observations can be guaranteed with high probability. In this paper, we show that Toeplitz-structured matrices with entries drawn independently from the same distributions are also sufficient to recover x from y with high probability, and we compare the performance of such matrices with that of fully independent and identically distributed ones. The use of Toeplitz matrices in CS applications has several potential advantages: (i) they require the generation of only O(n) independent random variables; (ii) multiplication with Toeplitz matrices can be efficiently implemented using fast Fourier transform, resulting in faster acquisition and reconstruction algorithms; and (iii) Toeplitz-structured matrices arise naturally in certain application areas such as system identification.
Starting Page	294
Ending Page	298
File Size	1014763
Page Count	5
File Format	PDF
ISBN	9781424411979
DOI	10.1109/SSP.2007.4301266
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-08-26
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Compressed sensing Signal processing Probability distribution Sparse matrices Data compression Image processing System identification Gas insulated transmission lines Optical computing Random variables underdetermined systems of linear equations restricted isometry property system identification Toeplitz matrices
Content Type	Text
Resource Type	Article

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