Feasible uniform-resolution penalized likelihood reconstruction for static- and multi-frame 3D PET

Penalized likelihood reconstruction provides the possibility to produce images with desirable features. However, in some dynamic applications where system sensitivity and emission distribution are spatially and temporally variant, simple quadratic regularization does not produce uniform resolution over space and time for multi-frame reconstructions. In this study, we extended the spatially-invariant resolution regularization method of Fessler et al. to accommodate static- and multi-frame reconstruction in 3D PET systems. The proposed regularizations, denoted as UR3D/M-UR3D, were compared with the original method (UR2D) in HRRT simulations and real phantom experiments, and showed superior performance. Specifically, in single-frame reconstructions, UR3D regularization reduced the axial-position-dependent resolution degradation seen in UR2D regularization. In multi-frame reconstructions, M-UR3D also achieved more consistent resolution recovery across frames for reconstructed point sources/line sources than the original method.