Finite Hilbert transform with incomplete data: null-space and singular values

    Authors

    A. Katsevich;A. Tovbis

    Comments

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    Abbreviated Journal Title

    Inverse Probl.

    Keywords

    CONE-BEAM CT; IMAGE-RECONSTRUCTION; VALUE DECOMPOSITION; Mathematics, Applied; Physics, Mathematical

    Abstract

    Using the Gelfand-Graev formula, the interior problem of tomography reduces to the inversion of the finite Hilbert transform (FHT) from incomplete data. In this paper, we study several aspects of inverting the FHT when the data are incomplete. Using the Cauchy transform and an approach based on the Riemann-Hilbert problem, we derive a differential operator that commutes with the FHT. Our second result is the characterization of the null-space of the FHT in the case of incomplete data. Also, we derive the asymptotics of the singular values of the FHT in three different cases of incomplete data.

    Journal Title

    Inverse Problems

    Volume

    28

    Issue/Number

    10

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    28

    WOS Identifier

    WOS:000310574000018

    ISSN

    0266-5611

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