Joint Estimation of Activity, Attenuation and Motion in Respiratory-Gated Time-of-Flight PET

In PET imaging, the patient’s respiratory motion during the scan is unavoidable and has an important impact on the quality of the reconstructed image, creating motion artifacts which can alter the clinical’s diagnosis. Correcting for these artefacts involves several challenges, in particular the estimation of the respiratory waveform and the design of an efficient motion corrected image reconstruction method. In this study we use a data-driven strategy to estimate the respiratory waveform, and then we developed a joint motion estimation and image reconstruction approach for TOF-PET. This joint approach reconstructs a unique 3D activity image at a "virtual" position and introduces non-smooth regularizations on the non-rigid displacements and the reconstructed activity image. This joint approach is based on the Alternating Directions Method of Multipliers (ADMM) which leads to several optimization sub-problems. These are solved with a Maximum A Posteriori estimation of the activity simultaneously with the estimation of the attenuation factors, and regularized non-parametric registrations to estimate displacements for each gate. We validated the method on experimental list-mode TOF-PET data obtained with the Siemens Biograph mCT PET/CT system and an anthropomorphic thorax phantom which simulates respiratory motion.