High resolution and better quantification by tube of response modelling in 3D PET reconstruction

In high resolution 3D PET it is possible to increase the reconstruction quality by precisely modelling the forward process of the measurement before trying to solve the inverse problem. A general framework is presented how positron range, scatter contributions and attenuation of the γ-rays can be integrated into the reconstruction process. Taking the TierPET scanner as an example, algorithms are presented how to derive the necessary properties. The area of the reconstruction volume contributing to a pair of detectors with unscattered events is called Tube of Response (TOR), while the area contributing the scattered events is called Scatter Volume of Response (SVOR). The elements of the system transfer matrix are calculated considering the geometry of the TORs. The scatter fraction is estimated by assuming single scatter and using an analytic derivation using the Klein-Nishina equation. The method was implemented with a 3D-Maximum Likelihood (ML) algorithm. Compared to a simplified modelling of the forward process, this approach yields better reconstructions of simulated point- and phantom sources in terms of quantification and spatial resolution