Analytical Geometric Model for Photon Coincidence Detection in 3D PET

The importance of the transition matrix has been recently pointed out by several research groups in 3D Positron Emission Tomography (PET) reconstruction. Analytical methods have become an alternative to Monte Carlo Simulations. In order to reduce the storage of this huge matrix and to make some calculations feasible it is possible to factorize this matrix. Each new factor matrix can incorporate different data acquisition effects but the geometric matrix is still the crux. We propose here and exact analytical 3D true solid angle of view model for the elements in this geometric transition matrix. Initial results suggest that some relevant differences could exist with some approximate models previously proposed to date.