A New Fully 3D Maximum Likelihood PET Reconstruction Applicable to Different Detector Arrangements

We developed a fully-3D, maximum likelihood based, PET reconstruction routine applicable to different coincidence detector arrangements for PET. It allows to study the influence of several γ-ray detector geometries onto the corresponding reconstructed images. The scope of this study is to optimize a tomograph to be fully dedicated to the monitoring of heavy ion tumor therapy with a rotating beam delivery (gantry). A special purpose routine was needed in order to surpass situations not approached before: (i) the low counting statistics acquired during therapy with carbon ions makes the application of already developed 3D iterative algorithms with 2D sampling modes impossible, (ii) a fixed dual head PET scanner provides a coincidence detector with spatial variant response, which forbids the application of the algebraic reconstruction methods used in nuclear medicine and (iii) for the unprecedent huge size of coincident channels both for a closed ring camera, or a dual head camera with a small gap, the direct application of the routine previously developed for the positron tomograph at the GSI treatment site [1] is not feasible (the number of possible coincidence channels increases from 4 to 170 million). The new routine first samples the list mode data into coincidence channels according to a self-developed channel factorizing scheme. This scheme, combined with direct memory allocation during runtime, feeds the rest of the reconstruction routine with a packed matrix Y containing only the measured data (no empty coincidence channels). The routine than processes Y to find the most probable image X with the maximum likelihood estimation maximization algorithm [2]: