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

    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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