MAP reconstruction for Fourier rebinned TOF-PET data

Bing Bai, Yanguang Lin, Wentao Zhu, Ran Ren, Quanzheng Li, Magnus Dahlbom, Frank DiFilippo, Richard M Leahy
2014 Physics in Medicine and Biology  
Time-of-flight (TOF) information improves signal to noise ratio in Positron Emission Tomography (PET). Computation cost in processing TOF-PET sinograms is substantially higher than for nonTOF data because the data in each line of response is divided among multiple time of flight bins. This additional cost has motivated research into methods for rebinning TOF data into lower dimensional representations that exploit redundancies inherent in TOF data. We have previously developed approximate
more » ... r methods that rebin TOF data into either 3D nonTOF or 2D nonTOF formats. We refer to these methods respectively as FORET-3D and FORET-2D. Here we describe maximum a posteriori (MAP) estimators for use with FORET rebinned data. We first derive approximate expressions for the variance of the rebinned data. We then use these results to rescale the data so that the variance and mean are approximately equal allowing us to use the Poisson likelihood model for MAP reconstruction. MAP reconstruction from these rebinned data uses a system matrix in which the detector response model accounts for the effects of rebinning. Using these methods we compare performance of FORET-2D and 3D with TOF and nonTOF reconstructions using phantom and clinical data. Our phantom results show a small loss in contrast recovery at matched noise levels using FORET compared to reconstruction from the original TOF data. Clinical examples show FORET images that are qualitatively similar to those obtained from the original TOF-PET data but a small increase in variance at matched resolution. Reconstruction time is reduced by a factor of 5 and 30 using FORET3D+MAP and FORET2D+MAP respectively compared to 3D TOF MAP, which makes these methods attractive for clinical applications.
doi:10.1088/0031-9155/59/4/925 pmid:24504374 pmcid:PMC3980855 fatcat:d3tno7joendmnlvnvl2k4wjlru