Resolution Modelling in Projection Space using Factorized Multi-block Detector Response Function

Abstract

Position emission tomography (PET) images usually suffer from low spatial resolution and signal-to-noise (SNR) ratio. The degradation of image resolution in PET is caused by detection process, e.g. inter-crystal scattering, crystal penetration. An Accurate Detector Response Functions (DRF) allows to model these phenomena and increase the spatial resolution as well as SNR in the iterative image reconstruction. However, fully 3D DRF for pixelated crystal arrays (block) which also considers inter-block penetration and inter-crystal scattering between different blocks still remains challenging. Here we demonstrate the development of an accurate DRF for the Siemens Hybrid MR-BrainPET system with a 9-block model using GATE simulations. Different incident γ rays are described by four parameters (x, y, θ, φ) in Block Coordinate System. Their detection response, comprising a list of fired crystals’ id and corresponding detection probability, are stored as an entry of a 4D Look-up Table (LUT) addressed by (x, y, θ, φ). Based on the DRF LUT, a PSF blurring kernel in 4D projection space can be obtained by combining two multi-block DRF according to the intersected block pair for each Line-of-Response. PSF modelling in projection space is implemented in the reconstruction toolkit PRESTO based on the developed DRF LUT. A resolution phantom with 6 types of hot rods is simulated by GATE and reconstructed by PRESTO with MLEM and MLEM-PSF. Visual results demonstrate that with moderate statistics (2.8×108), MLEM-PSF could recover small bins (5 mm) at the edge of FOV in a more accurate way compared to MLEM. Furthermore, the images of MLEM-PSF show better noise suppression.