INVERSION FORMULAE FOR THE cosh-WEIGHTED HILBERT TRANSFORM

    Authors

    M. Bertola; A. Katsevich;A. Tovbis

    Comments

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    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    CONE-BEAM CT; IMAGE-RECONSTRUCTION; Mathematics, Applied; Mathematics

    Abstract

    In this paper we develop formulae for inverting the so-called cosh-weighted Hilbert transform H-mu, which arises in Single Photon Emission Computed Tomography (SPECT). The formulae are theoretically exact, require a minimal amount of data, and are similar to the classical inversion formulae for the finite Hilbert transform (FHT) H-0. We also find the null-space and the range of H-mu in L-p with p > 1. Similarly to the FHT, the null-space turns out to be one-dimensional in L-p for any p. (1, 2) and trivial - for p > = 2. We prove that H-mu is a Fredholm operator of index - 1 when it acts between the L-p spaces, p is an element of (1, infinity), p not equal 2. Finally, in the case where p = 2 we find the range condition for H-mu, which is similar to that for the FHT H-0. Our work is based on the method of the Riemann-Hilbert problem.

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    141

    Issue/Number

    8

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    2703

    Last Page

    2718

    WOS Identifier

    WOS:000326573000016

    ISSN

    0002-9939

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