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Sampling in Parallel-Beam Tomography

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Inverse Problems, Tomography, and Image Processing

Abstract

We present Shannon sampling theory for functions defined on \(T \times \mathbb{R} \) × ℝ, where T denotes the circle group, prove a new estimate for the aliasing error, and apply the result to parallel-beam diffraction tomography. The class of admissible sampling lattices is characterized and general sampling conditions are derived which lead to the identification of new efficient sampling schemes. Corresponding results for x-ray tomography are obtained in the high-frequency limit.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Oregon State University, Corvallis, OR, USA

    Adel Faridani

Authors
  1. Adel Faridani
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Editor information

Editors and Affiliations

  1. Kansas State University, Manhattan, Kansas, USA

    Alexander G. Ramm

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© 1998 Springer Science+Business Media New York

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Faridani, A. (1998). Sampling in Parallel-Beam Tomography. In: Ramm, A.G. (eds) Inverse Problems, Tomography, and Image Processing. Springer, Boston, MA. https://doi.org/10.1007/978-1-4020-7975-7_3

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  • DOI: https://doi.org/10.1007/978-1-4020-7975-7_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1900-7

  • Online ISBN: 978-1-4020-7975-7

  • eBook Packages: Springer Book Archive

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