Statistical reconstruction methods in PET: resolution limit, noise, edge artifacts and considerations for the design of better scanners

Small animal positron emission tomography (PET) scanners are being increasingly used as a basic measurement tool in modern biomedical research. The new designs and technologies of these scanners and the modern reconstruction methods have allowed to reach high spatial resolution and sensitivity. Despite their successes, some important issues remain to be addressed in high resolution PET imaging. First, iterative reconstruction methods like maximum likelihood-expectation maximization (MLEM) are known to recover resolution, but also to create noisy images and edge artifacts if some kind of regularization is not imposed. Second, the limit of resolution achievable by iterative methods on high resolution scanners is not quantitatively understood. Third, the use of regularization methods like Sieves or maximum a posteriori (MAP) requires the determination of the optimal values of several adjustable parameter that may be object-dependent. In this work we review these problems in high resolution PET and establish that the origin of them is more related with the physical effects involved in the emission and detection of the radiation during the acquisition than with the kind of iterative reconstruction method chosen. These physical effects (positron range, non-collinearity, scatter inside the object and inside the detector materials) cause that the tube of response (TOR) that connects the voxels with a line of response (LOR) is rather thick. This implies that the higher frequencies of the patient organ structures are not recorded by the scanner and therefore cannot be recovered during the reconstruction. As iterations grow, ML-EM algorithms try to recover higher frequencies in the image. Once that a certain critic frequency is reached, this only maximizes high frequency noise. Using frequency response analyses techniques, we determine the maximum achievable resolution, before edge artifacts spoil the quality of the image, for a particular scanner as a function of the thickness of the TOR, and independently of the reconstruction method employed. With the same techniques, we can deduce well defined stopping criteria for reconstructions methods. Also, criteria for the highest number of subsets which should be used and how the design of the scanners can be optimized when statistical reconstruction methods are employed, is established.