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

Abstract

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
Volume34
Issue number2
Number of pages15
ISSN0266-5611
DOIs
Publication statusPublished - 2018

Cite this

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title = "A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation: Paper",
abstract = "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.",
author = "I.G. Kazantsev and Olsen, {Ulrik Lund} and Poulsen, {Henning Friis} and Hansen, {Per Christian}",
year = "2018",
doi = "10.1088/1361-6420/aaa05d",
language = "English",
volume = "34",
journal = "Inverse Problems",
issn = "0266-5611",
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A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation : Paper. / Kazantsev, I.G.; Olsen, Ulrik Lund; Poulsen, Henning Friis; Hansen, Per Christian.

In: Inverse Problems, Vol. 34, No. 2, 024002 , 2018.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation

T2 - Paper

AU - Kazantsev, I.G.

AU - Olsen, Ulrik Lund

AU - Poulsen, Henning Friis

AU - Hansen, Per Christian

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

U2 - 10.1088/1361-6420/aaa05d

DO - 10.1088/1361-6420/aaa05d

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VL - 34

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

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