Title

Filtered backprojection inversion of the cone beam transform for a general class of curves

Authors

Authors

A. Katsevich;M. Kapralov

Comments

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Abbreviated Journal Title

SIAM J. Appl. Math.

Keywords

shift-invariant filtering; theoretically exact; PI lines; LONG-OBJECT PROBLEM; IMAGE-RECONSTRUCTION; COMPUTED-TOMOGRAPHY; SPIRAL; CT; ALGORITHM; PROJECTION; CIRCLE; PITCH; Mathematics, Applied

Abstract

We extend a cone beam transform inversion formula, proposed earlier for helices by one of the authors, to a general class of curves. The inversion formula remains efficient, because filtering is shift-invariant and is performed along a one-parametric family of lines. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much, and do not admit lines which are tangent to C at one point and intersect C at another point. The notions of PI lines and PI segments are generalized, and their properties are studied. The domain U is found, where PI lines are guaranteed to be unique. Results of numerical experiments demonstrate very good image quality.

Journal Title

Siam Journal on Applied Mathematics

Volume

68

Issue/Number

2

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

334

Last Page

353

WOS Identifier

WOS:000251836700002

ISSN

0036-1399

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