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Mathematical Methods in PET and SPECT Imaging

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Handbook of Mathematical Methods in Imaging

Abstract

In this chapter, we present the mathematical formulation of the inverse Radon transform and of the inverse attenuated Radon transform (IART), which are used in PET and SPECT image reconstruction, respectively. Using a new method for deriving transform pairs in one and two dimensions, we derive the inverse Radon transform and the IART. Furthermore, we discuss an alternative approach for computing the Hilbert transform using cubic splines. This new approach, which is referred to as spline reconstruction technique, is formulated in the physical space, in contrast to the well-known filtered backprojection (FBP) algorithm which is formulated in the Fourier space. Finally, we present the results of several rigorous studies comparing FBP with SRT for PET. These studies, which use both simulated and real data and which employ a variety of image quality measures including contrast and bias, indicate that SRT has certain advantages in comparison with FBP.

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Authors and Affiliations

  1. University of Technology Darmstadt, Darmstadt, Germany

    Athanasios S. Fokas

  2. Research Center of Mathematics, Academy of Athens, Soranou Efessiou 4, 11527, Athens, Greece

    George A. Kastis

Authors
  1. Athanasios S. Fokas
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  2. George A. Kastis
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Correspondence to Athanasios S. Fokas .

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Editors and Affiliations

  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

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Fokas, A.S., Kastis, G.A. (2015). Mathematical Methods in PET and SPECT Imaging. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_45

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