A box spline calculus for computed tomography

Authors:
Alireza Entezari;Michael Unser
Affiliations:
CISE Department, University of Florida, Gainesville, FL;EPFL, Lausanne, Switzerland
Venue:
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Year:
2010

Citing 5
Cited 1

A spline inversion formula for the Radon transform

SIAM Journal on Numerical Analysis
Box splines

Box splines
Use of box splines in computer tomography

Computing
The mathematics of computerized tomography

The mathematics of computerized tomography
Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice

IEEE Transactions on Visualization and Computer Graphics

Voronoi splines

IEEE Transactions on Signal Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.