Comparison of different reconstruction methods for planar images in small gamma cameras

In this work we present a comparison of different methods for reconstructing the position of the events detected by gamma cameras with small Field of View. This task was completed within a project aimed to the development of an ultra high resolution, MR compatible PET detector camera head based on SiPM detector. It is well known that the spatial resolution deteriorates and the displacement error (defined as the deviation of the reconstructed position from the true position) increases at the edges of the detector. Here we investigate the possibility of improving the detector performance by using different reconstruction methods. The usual algorithm based on the barycenter fails to track the true position near the edges of the detector. We implemented and tested four different algorithms: the classic barycenter, a modified barycenter method where we consider not the charge collected, but the charge squared (named ``barycenter squared''), an algorithm based on the estimation of the skewness of the distribution of the light (``skewness''), and finally a method based on the minimization of the difference between the distribution of light and a suitable fitting function (``Newton''). It turns out that the use of reconstruction algorithms different from the classic barycenter can help to improve the performance of the system. In particular, the reconstruction error improves, especially at the edges of the detector. Our simulations show that it is feasible to get submillimeter planar spatial resolutions at the center of the detector and of about 1 mm at the edges of the detector.