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conference paper

A Box Spline Calculus for Computed Tomography

Entezari, A.
•
Unser, M.  
2010
Proceedings of the Seventh IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'10)

B-splines are attractive basis functions for the continuous-domain representation of biomedical images and volumes. In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their transforms. Our results are general; they cover all known brands of compactly-supported box splines (tensor-product B-splines, separable or not) in any dimensions. In particular, we prove that the 2-D Radon transform of an N-direction box spline is generally a (non-uniform) polynomial spline of degree N − 1. The proposed framework allows for a proper discretization of a variety of 2-D and 3-D tomographic reconstruction problems in a box spline basis. It is of relevance for imaging modalities such as X-ray computed tomography and 3-D cryo-electron microscopy.

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Type
conference paper
DOI
10.1109/ISBI.2010.5490105
Author(s)
Entezari, A.
Unser, M.  
Date Issued

2010

Publisher

IEEE

Published in
Proceedings of the Seventh IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'10)
Issue

Rotterdam, The Netherlands

Start page

600

End page

603

URL

URL

http://bigwww.epfl.ch/publications/entezari1001.html

URL

http://bigwww.epfl.ch/publications/entezari1001.pdf

URL

http://bigwww.epfl.ch/publications/entezari1001.ps
Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LIB  
Available on Infoscience
September 18, 2015
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/118167
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