A box spline calculus for computed tomography

Alireza Entezari, Michael Unser
2010 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro  
B-splines are attractive basis functions for the continuousdomain 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 (tensorproduct B-splines, separable or not) in any dimensions. In particular, we prove that the 2-D Radon transform of an Ndirection box spline
more » ... rection 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.
doi:10.1109/isbi.2010.5490105 dblp:conf/isbi/EntezariU10 fatcat:67stwgonvfejnnwdgpzn3dnob4