Title

An accurate approximate algorithm for motion compensation in two-dimensional tomography

Authors

Authors

A. Katsevich

Comments

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Abbreviated Journal Title

Inverse Probl.

Keywords

GENERALIZED RADON-TRANSFORM; RECONSTRUCTION; PLANE; FIELD; Mathematics, Applied; Physics, Mathematical

Abstract

In this paper, we propose two approximate inversion formulae for motion compensation in tomography: for parallel beam and fan beam geometries. Let epsilon denote the operator, which corresponds to the error term of an inversion formula. It is proven that in both cases epsilon : H(0)(m) -> H(0)(m+1) is bounded; thus, the error term is one order smoother than the original function f in the scale of Sobolev spaces. It is also proven that in both cases if the motion map approaches the identity map, then the norm of epsilon approaches zero. The formulae can be easily implemented numerically. Results of numerical experiments in the fan-beam case (which is more common in applications) demonstrate good image quality even when motion is relatively strong.

Journal Title

Inverse Problems

Volume

26

Issue/Number

6

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

16

WOS Identifier

WOS:000277968800007

ISSN

0266-5611

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