A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation. (10th January 2018)

• Record Type: Journal Article
• Authors: Kazantsev, I G; Olsen, U L; Poulsen, H F; Hansen, P C
• Is Part Of: Inverse problems. Volume 34:Number 2(2018:Feb.)
• Publication Date: 2018-01-10
• Subjects: PET -- Compton scatter -- integral transforms -- slice-by-slice convolution -- reconstruction; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaa05d
• Languages: English
• ISSNs: 0266-5611

Abstract

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.