Broken ray transform: inversion and a range condition

    Authors

    A. Katsevich;R. Krylov

    Comments

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    Abbreviated Journal Title

    Inverse Probl.

    Keywords

    Mathematics, Applied; Physics, Mathematical

    Abstract

    In this paper we study a class of broken ray transforms (BRT), which can be implemented with flat and/or curved detectors. In the case of two detectors we obtain an inversion formula, which involves a second-order derivative of the data and integration along characteristics. In the case of three detectors, we obtain an inversion formula, which is purely local and involves only the first-order derivatives of the data. Hence the formula solves the interior problem. Neither the object nor the source and detectors require to be rotated in order to obtain a complete data set. We also prove a theorem, which describes the range of the BRT in the case of three detectors. Finally, the results of numerical experiments are presented.

    Journal Title

    Inverse Problems

    Volume

    29

    Issue/Number

    7

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    15

    WOS Identifier

    WOS:000321183800008

    ISSN

    0266-5611

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