Stability estimates for helical computer tomography

    Authors

    A. Katsevich

    Comments

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    Abbreviated Journal Title

    J. Fourier Anal. Appl.

    Keywords

    cone-beam; helical tomography; inversion; extension to distributions; stability estimates; Sobolev spaces; microlocal analysis; X-RAY TRANSFORM; CONE-BEAM TOMOGRAPHY; RADON TRANSFORMS; RECONSTRUCTION; ALGORITHM; Mathematics, Applied

    Abstract

    In this article we analyze an inversion formula for helical computer tomography proposed earlier by the author. Our first result is a global stability estimate. The formula is continuous of order I in the Sobolev norms. Then the formula is extended to distributions. Originally it was derived only for C-0(infinity) functions. It turns out that there exist distributions, to which the formula does not apply. These exceptional distributions are characterized in terms of their wave fronts. Finally, we show that microlocally away from a critical set the continuity estimate can be improved: The order goes down from 1 to 1/2.

    Journal Title

    Journal of Fourier Analysis and Applications

    Volume

    11

    Issue/Number

    1

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    85

    Last Page

    105

    WOS Identifier

    WOS:000228049500005

    ISSN

    1069-5869

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