A general scheme for constructing inversion algorithms for cone beam CT
type: Item
instance of: scholarly article
title: A general scheme for constructing inversion algorithms for cone beam CT
zbMATH Open document ID: 1079.44500
DOI: 10.1155/S0161171203209315
author: A. Katsevich
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/52006
review text: Summary: Given a rather general weight function \(n_0\), we derive a new cone beam transform inversion formula. The derivation is explicitly based on Grangeat's formula (1990) and the classical 3D Radon transform inversion. The new formula is theoretically exact and is represented by a 2D integral. We show that if the source trajectory \(C\) is complete in the sense of Tuy (1983) (and satisfies two other very mild assumptions), then substituting the simplest weight \(n_0\equiv 1\) gives a convolution-based FBP algorithm. However, this easy choice is not always optimal from the point of view of practical applications. The weight \(n_0\equiv 1\) works well for closed trajectories, but the resulting algorithm does not solve the long object problem if \(C\) is not closed. In the latter case one has to use the flexibility in choosing \(n_0\) and find the weight that gives an inversion formula with the desired properties. We show how this can be done for spiral CT. It turns out that the two inversion algorithms for spiral CT proposed earlier by the author are particular cases of the new formula. For general trajectories the choice of weight should be done on a case-by-case basis.
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 1930030
MaRDI profile type: Publication
Wikidata QID: Q124767480
description: scientific article; zbMATH DE number 1930030