A Bregman Majorization-Minimization Framework for Pet Image Reconstruction

Positron emission tomography (PET) is a quantitative imaging modality widely used in oncology, neurology, and pharmacology. The data acquired by a PET scanner correspond to projections of the concentration activity, assumed to follow a Poisson distribution. The reconstruction of images from tomographic projections corrupted by Poisson noise is a challenging ill-posed large-scale inverse problem. Several available solvers use the majorization-minimization (MM) principle, though relying on various construction strategies with a lack of unifying framework. This work fills the gap by introducing the concept of Bregman majorization. This leads to a unified view of MM-based methods for image reconstruction in the presence of Poisson noise. From this general approach, we exhibit three algorithmic solutions and compare their computational efficiency on a problem of dynamic PET image reconstruction, either using GPU or CPU processing.