A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation: Paper

I.G. Kazantsev*, Ulrik Lund Olsen, Henning Friis Poulsen, Per Christian Hansen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


We investigate the idealized mathematical model of single scatter in PET for a detector system possessing excellent energy resolution. The model has the form of integral transforms estimating the distribution of photons undergoing a single Compton scattering with a certain angle. The total single scatter is interpreted as the volume integral over scatter points that constitute a rotation body with a football shape, while single scattering with a certain angle is evaluated as the surface integral over the boundary of the rotation body. The equations for total and sample single scatter calculations are derived using a single scatter simulation approximation. We show that the three-dimensional slice-by-slice filtered backprojection algorithm is applicable for scatter data inversion provided that the attenuation map is assumed to be constant. The results of the numerical experiments are presented.
Original languageEnglish
Article number024002
JournalInverse Problems
Issue number2
Number of pages15
Publication statusPublished - 2018

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