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Image Reconstruction for Positron Emission Tomography Based on Chebyshev Polynomials

In: Approximation and Computation in Science and Engineering

Author

Listed:
  • George Fragoyiannis

    (University of Patras)

  • Athena Papargiri

    (University of Patras)

  • Vassilis Kalantonis

    (University of Patras)

  • Michael Doschoris

    (Leibniz Institute for Farm Animal Biology)

  • Panayiotis Vafeas

    (University of Patras)

Abstract

The study of the functional characteristics of the brain plays a crucial role in modern medical imaging. An important and effective nuclear medicine technique is positron emission tomography (PET), whose utility is based upon the noninvasive measure of the in vivo distribution of imaging agents, which are labeled with positron-emitting radionuclides. The main mathematical problem of PET involves the inverse Radon transform, leading to the development of several methods toward this direction. Herein, we present an improved formulation based on Chebyshev polynomials, according to which a novel numerical algorithm is employed in order to interpolate exact simulated values of the Randon transform via an analytical Shepp–Logan phantom representation. This approach appears to be efficient in calculating the Hilbert transform and its derivative, being incorporated within the final analytical formulae. The numerical tests are validated by comparing the presented methodology to the well-known spline reconstruction technique.

Suggested Citation

  • George Fragoyiannis & Athena Papargiri & Vassilis Kalantonis & Michael Doschoris & Panayiotis Vafeas, 2022. "Image Reconstruction for Positron Emission Tomography Based on Chebyshev Polynomials," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Approximation and Computation in Science and Engineering, pages 281-295, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84122-5_16
    DOI: 10.1007/978-3-030-84122-5_16
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