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

Stabilized inversion for limited angle tomography

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)
Olson, T. ; Dept. of Math., Dartmouth Coll., Hanover, NH, USA

Many problems in applied mathematics involve recovering a function f from measurements of Lf, where L is a known operator. We study the recovery of a function from limited knowledge of its Fourier transform. The inversion of a compact operator L (for limited data) is considered from a discrete signal processing perspective. In this context, the continuous operator L is naturally viewed as the limiting case of a series of discrete operators. Since L will generally be compact and self-adjoint, its spectrum can be analyzed via standard techniques. Real-world problems are generated from discretely sampled data sets. Therefore, we believe that it is more informative to study the spectra of the discrete approximations to L rather than the spectrum of L itself. Our main tool for analyzing the spectra of these discrete approximations to L is the theory of finite Toeplitz forms, originally introduced by Szego (1915). We show that the study of these finite Toeplitz forms give us some clues concerning the construction of an accurate, stable inversion for L, even when the continuous spectra of L suggests that it is not invertible

Published in:

Engineering in Medicine and Biology Magazine, IEEE  (Volume:14 ,  Issue: 5 )

Date of Publication:

Sep/Oct 1995

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.