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Mathematical Methods in PET and SPECT Imaging

In: Handbook of Mathematical Methods in Imaging

Author

Listed:
  • Athanasios S. Fokas

    (University of Technology Darmstadt)

  • George A. Kastis

    (Academy of Athens, Research Center of Mathematics)

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.

Suggested Citation

  • Athanasios S. Fokas & George A. Kastis, 2015. "Mathematical Methods in PET and SPECT Imaging," Springer Books, in: Otmar Scherzer (ed.), Handbook of Mathematical Methods in Imaging, edition 2, pages 903-936, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0790-8_45
    DOI: 10.1007/978-1-4939-0790-8_45
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