Detector response correction for 3D PET using Bayesian modeling of the location Of interaction

The unknown exact locations of the interaction (LOI) of photons within detector crystals is a major contribution to the loss of resolution in PET imaging. This effect is intensified with larger distances of the objects from the center of the field-of-view of the camera. In this work we propose a method that recover the loss of the resolution due to unknown LOI. The new method is an unique approach defined in Bayesian framework where the LOIs for two annihilation photons are modeled within the crystal volumes in which they were detected. LOI for each detected event is modeled independently, therefore that method works for binned and list-mode data. The approach was implemented for the minimum-mean-square-error (MMSE) estimator of the number of emissions per voxel. The Markov Chain Monte Carlo origin ensemble algorithm to find the estimator from the projection data was used. We performed computer simulations in 3D using Monte Carlo software of the data acquisitions and simulated Siemens Biograph PET scanner. We used small hot lesion phantom with nine 0.5 cm in diameter spheres placed in warm background. We found that compared to reconstructions with known LOIs for which we assumed that no loss of resolution occurred due to unknown LOI, the correction method proposed in this paper recovered the contrast for investigated object positioned in the center of the scanner. The contrast was only 80% recovered for the phantom positioned off-center due to suboptimal modeling of the LOIs. As expected, an increase in apparent noise in the reconstructed image was observed. This was especially evident for the background region. The method is a novel approach that can be used to improve the spatial resolution of images obtained by PET scanners. The method is directly applicable to time-of-flight PET.