Incorporation of position dependent detection probability into a tube-of-response based model for system matrix calculation in 3D PET imagereconstruction

Ziel/Aim:

We have presented previously a model for fast on-the-fly volume-of-intersection (VOI) system matrix calculation for PET image reconstruction. The model replaces cubic voxels by spheres and the usual line of response by a cylindrical tube of response (TOR) whose diameter matches the size of the detector crystals. We now present a refined model which takes into account solid angle effects and position dependent detection efficiency across the crystal surface by using a TOR with a position-variant density.

Methodik/Methods:

We model the detection efficiency across the crystal surface as a radially symmetric function (superposition of two error functions) which leads to a TOR with a variable radial density. Additionally accounting for the solid angle effects results in a further modification of the TOR density that also varies in the axial direction. Consequently, the density-weighted VOI between TOR and spherical voxel now depends not only on the distance between the center of spherical voxel and line of TOR but also on the axial position along the TOR. The new model was integrated into our Tube-Of-Response High Resolution OSEM Reconstruction (THOR) and evaluated using a cylindrical phantom with spherical inserts. We have investigated several figures of merit (reconstructed spatial resolution, noise level, extend of Gibbs artifacts) and compared them between the original and modified TOR models.

Ergebnisse/Results:

The modified model maintains the high spatial resolution already demonstrated for the original TOR approach while showing an improved noise characteristics and reduction of residual Gibbs artifacts. The improvement of image quality overall is only modest.

Schlussfolgerungen/Conclusions:

The proposed modification of the TOR model for on-the-fly system matrix computation allows more accurate modelling of the scanner geometry and event detection and leads to reduced noise levels and Gibbs artifacts in the reconstructed image. However, it noticeably increases reconstruction times in comparison to the original model.