Fast inversion of the Radon transform using log-polar coordinates and partial back-projections
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/244610
- author
- Andersson, Fredrik LU
- organization
- publishing date
- 2005
- 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
- Society for Industrial and Applied Mathematics
- 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
- 2016-04-01 17:08:05
- date last changed
- 2022-02-20 18:53:20
@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}},
keywords = {{Radon transform; filtered back-projection}},
language = {{eng}},
number = {{3}},
pages = {{818--837}},
publisher = {{Society for Industrial and Applied Mathematics}},
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}},
doi = {{10.1137/S0036139903436005}},
volume = {{65}},
year = {{2005}},
}