Accurate 2D Reconstruction for PET Scanners based on the Analytical White Image Model

TL;DR

This paper introduces an accurate analytical model for the white image in PET scanners, enabling improved image reconstruction by integrating it into a modified MLEM algorithm that outperforms non-compensated methods.

Contribution

The paper presents a novel closed-form analytical model of the crystal response in PET scanners and integrates it into a ray-driven MLEM reconstruction algorithm.

Findings

The model accurately approximates the crystal response with insignificant error.

The integrated reconstruction method outperforms non-compensated approaches.

Validated on synthetic and real data with small animal PET scanners.

Abstract

In this paper, we provide a precise mathematical model of crystal-to-crystal response which is used to generate the white image - a necessary compensation model needed to overcome the physical limitations of the PET scanner. We present a closed-form solution, as well as several accurate approximations, due to the complexity of the exact mathematical expressions. We prove, experimentally and analytically, that the difference between the best approximations and real crystal-to-crystal response is insignificant. The obtained responses are used to generate the white image compensation model. It can be written as a single closed-form expression making it easy to implement in known reconstruction methods. The maximum likelihood expectation maximization (MLEM) algorithm is modified and our white image model is integrated into it. The modified MLEM algorithm is not based on the system matrix, rather it is based on ray-driven projections and back-projections. The compensation model provides all necessary information about the system. Finally, we check our approach on synthetic and real data. For the real-world acquisition, we use the Raytest ClearPET camera for small animals and the NEMA NU 4-2008 phantom. The proposed approach overperforms competitive, non-compensated reconstruction methods.