Piecewise Polynomial Inversion of the Radon Transform in Three Space Dimensions via Plane Integration and Applications in Positron Emission Tomography

Nicholas E. Protonotarios (), George A. Kastis (), Nikolaos Dikaios () and Athanassios S. Fokas ()
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Nicholas E. Protonotarios: University of Cambridge
George A. Kastis: Academy of Athens
Nikolaos Dikaios: Academy of Athens
Athanassios S. Fokas: University of Cambridge

A chapter in Nonlinear Analysis, Differential Equations, and Applications, 2021, pp 381-396 from Springer

Abstract: Abstract The inversion of the celebrated Radon transform in three dimensions involves two-dimensional plane integration. This inversion provides the mathematical foundation of the important field of medical imaging, known as three-dimensional positron emission tomography (3D PET). In this chapter, we present an analytical expression for the inversion of the three-dimensional Radon transform, as well as a novel numerical implementation of this formula, based on piecewise polynomials of the third degree.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-72563-1_17

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DOI: 10.1007/978-3-030-72563-1_17

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