On the relation between blob and tube-of-response based approaches to system matrix calculation in PET

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 (LOR) by a cylindrical tube of response (TOR). The use of spherically symmetric voxel makes it superficially similar to the blob model, where tracer distribution is discretized using modified Kaiser-Bessel window functions (KBWF) rather than cubic voxels. We now present an extended TOR model with radially varying tube density (eTOR) and investigate the relation between eTOR and the blob model. We also analyse under which conditions they can be mapped to each other and which density function leads to the best mapping.
Methodik/Methods:
We start with an analyses of circumstances under which both models generate equivalent system matrices. For that we investigate weighting functions of both models (Length of Intersection between LOR and blob and VOI between
TOR and sphere as functions of the impact parameter, respectively). We tried several candidate TOR density functions (Gaussian, difference of error functions and modified KBWF) and determined optimal parameters for the density
functions by least squares fitting of the respective TOR weighting function to the targeted weighting function of the blob model. Both, eTOR and blob models, were evaluated (using phantom data acquired on the Philips Ingenuity TF PET/MR system) regarding reconstructed resolution and noise level.
Ergebnisse/Results:
A good concordance between eTOR and blob model weighting functions can be achieved with all candidate functions. The best fit (residuals <5e-4) was obtained for KBWF. As expected, the close equivalence between the
weighting functions resulted in almost identical reconstructed resolution and noise level for all investigated voxel sizes and contrast ratios.
Schlussfolgerungen/Conclusions:
We analysed different density function for eTOR models and showed that all of them can be used to mimic (with high accuracy) the conventional blob model, proving a generic nature of the eTOR approach. The achieved equivalence of the weighting functions between eTOR and blob models also indicates that the conventional resampling step of the blob model might be unnecessary.