New iterative reconstruction methods for fan-beam tomography

Daniil Kazantsev, Valery Pickalov

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    Abstract

    In this paper, we present a novel class of iterative reconstruction methods for severely angular undersampled or/and limited-view tomographic problems with fan-beam scanning geometry. The proposed algorithms are based on a new analytical transform which generalizes Fourier-slice theorem to divergent-beam scanning geometries. Using a non-rigid coordinate transform, divergent rays can be reorganized into parallel ones. Therefore, one can employ a simpler parallel-beam projection model instead of more complicated divergent-beam geometries. Various existing iterative reconstruction techniques for divergent-beam geometries can be easily adapted to the proposed framework. The significant advantage of this formulation is the possibility of exploiting efficient Fourier-based recovery methods without rebinning of the projections. In case of highly sparse measurements (few-view data), rebinning methods are not suitable due to error-prone angular interpolation involved. In this work, three new methods based on the novel analytical framework for fan-beam geometry are presented: the Gerchberg-Papoulis algorithm, the Neumann decomposition method and its total variation regularized version. Presented numerical experiments demonstrate that the methods can be competitive in reconstructing from few-view noisy tomographic measurements.

    Original languageEnglish
    Pages (from-to)1-19
    Number of pages19
    JournalInverse Problems in Science and Engineering
    Early online date19 Jun 2017
    DOIs
    Publication statusPublished - 2017

    Keywords

    • computational methods
    • few-view
    • Fourier methods
    • integral equations
    • inverse problems
    • numerical solutions
    • Radon transform
    • tomography

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