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Fast inversion of the Radon transform using log-polar coordinates and partial back-projections

Andersson, Fredrik LU (2005) In SIAM Journal on Applied Mathematics 65(3). p.818-837
Abstract
In this paper a novel filtered back-projection algorithm for inversion of a discretized Radon transform is presented. It makes use of invariance properties possessed by both the Radon transform and its dual. By switching to log-polar coordinates, both operators can be expressed in a displacement invariant manner. Explicit expressions for the corresponding transfer functions are calculated. Furthermore, by dividing the back-projection into several partial back-projections, inversion can be performed by means of finite convolutions and hence implemented by an FFT-algorithm. In this way, a fast and accurate reconstruction method is obtained.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Radon transform, filtered back-projection
in
SIAM Journal on Applied Mathematics
volume
65
issue
3
pages
818 - 837
publisher
SIAM Publications
external identifiers
  • wos:000228468000005
  • scopus:21244456920
ISSN
0036-1399
DOI
10.1137/S0036139903436005
language
English
LU publication?
yes
id
b2fef281-66ce-4c3c-b119-feea5da91fcc (old id 244610)
alternative location
http://epubs.siam.org/sam-bin/dbq/article/43600
date added to LUP
2007-08-13 11:42:11
date last changed
2017-05-28 04:29:58
@article{b2fef281-66ce-4c3c-b119-feea5da91fcc,
  abstract     = {In this paper a novel filtered back-projection algorithm for inversion of a discretized Radon transform is presented. It makes use of invariance properties possessed by both the Radon transform and its dual. By switching to log-polar coordinates, both operators can be expressed in a displacement invariant manner. Explicit expressions for the corresponding transfer functions are calculated. Furthermore, by dividing the back-projection into several partial back-projections, inversion can be performed by means of finite convolutions and hence implemented by an FFT-algorithm. In this way, a fast and accurate reconstruction method is obtained.},
  author       = {Andersson, Fredrik},
  issn         = {0036-1399},
  keyword      = {Radon transform,filtered back-projection},
  language     = {eng},
  number       = {3},
  pages        = {818--837},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Applied Mathematics},
  title        = {Fast inversion of the Radon transform using log-polar coordinates and partial back-projections},
  url          = {http://dx.doi.org/10.1137/S0036139903436005},
  volume       = {65},
  year         = {2005},
}