Singular value decomposition for the truncated Hilbert transform

    Authors

    A. Katsevich

    Comments

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    Abbreviated Journal Title

    Inverse Probl.

    Keywords

    CONE-BEAM CT; IMAGE-RECONSTRUCTION; RADON-TRANSFORM; Mathematics, Applied; Physics, Mathematical

    Abstract

    Starting from a breakthrough result by Gelfand and Graev, inversion of the Hilbert transform became a very important tool for image reconstruction in tomography. In particular, their result is useful when the tomographic data are truncated and one deals with an interior problem. As was established recently, the interior problem admits a stable and unique solution when some a priori information about the object being scanned is available. The most common approach to solving the interior problem is based on converting it to the Hilbert transform and performing analytic continuation. Depending on what type of tomographic data are available, one gets different Hilbert inversion problems. In this paper, we consider two such problems and establish singular value decomposition for the operators involved. We also propose algorithms for performing analytic continuation.

    Journal Title

    Inverse Problems

    Volume

    26

    Issue/Number

    11

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    12

    WOS Identifier

    WOS:000283054000011

    ISSN

    0266-5611

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