Cone beam local tomography

    Authors

    A. Katsevich

    Comments

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    Abbreviated Journal Title

    SIAM J. Appl. Math.

    Keywords

    spiral CT; cone-beam data; local tomography; pseudodifferential; operators; singularities; artifacts; X-RAY TRANSFORM; SUFFICIENT CONDITIONS; RECONSTRUCTION; ALGORITHM; Mathematics, Applied

    Abstract

    In this paper we study three-dimensional cone beam local tomography. We analyze the local tomography function f(Lambda)(c), which was proposed earlier in [A.K. Louis and P. Maass, IEEE Trans. Medical Imaging, 12 (1993), pp. 764-769]. Let f be an unknown density distribution inside an object being scanned. We find a relationship between the wave fronts of f(Lambda)(c) and f and compute the principal symbol of the operator which maps f into f(Lambda)(c). Our results prove the fact, which was first noted in Louis and Maass, that one can recover most of the singularities of f knowing f(Lambda)(c). It is shown that these are precisely the singularities of f that are visible from the data. A simple and efficient algorithm for finding values of jumps of f knowing local cone beam data is proposed. The nature of artifacts inherent in cone beam local tomography is studied.

    Journal Title

    Siam Journal on Applied Mathematics

    Volume

    59

    Issue/Number

    6

    Publication Date

    1-1-1999

    Document Type

    Article

    Language

    English

    First Page

    2224

    Last Page

    2246

    WOS Identifier

    WOS:000083607800013

    ISSN

    0036-1399

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