Compact representation of PET 3D system response matrices

We present a method for the compact storage of 3D geometric system response matrix coefficients in PET, using a separation into transaxial and axial contributions. The pre-calculated geometric system response matrix may then be included in a factorized system response matrix formulation, within a model-based fully 3D iterative reconstruction algorithm. A related method is presented which applies this technique to 3D attenuation correction in PET, or to 3D transmission tomography. Separation of the problem into transaxial and axial components allows for more compact storage with less reliance on rebinning, mashing, or assumed symmetries in the detector geometry than is the case in alternative factorized formulations. The reduction in storage requirements may be used to efficiently and accurately incorporate blurring effects into the system response matrix formulation.