Mathematical Methods in PET and SPECT Imaging

Reference work entry

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.

Keywords

Hydroxyl Lymphoma Attenuation Estrogen Dopamine 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.University of Technology DarmstadtDarmstadtGermany
  2. 2.Research Center of MathematicsAcademy of AthensAthensGreece

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