Combined motion compensation and reconstruction for PET

We propose a new intrinsic motion-compensation algorithm for PET called "Blind Motion Compensated Reconstruction" (BMCR). BMCR is able to deal frames of extremely low statistics in the case of smooth motion. This is achieved by combining image reconstruction and motion compensation into one mathematical framework which consists of a cost functional and an optimization method. The cost functional basically consists of a ditTerence term which ensures consistency of the estimated parameters to the model and some regularization terms which render the problem mathematically well-posed. The optimization method aims at finding a pair of image and transformation/motion such that the cost functional is minimal. Up to now, for motion only translations are considered. Initial results are promising and show that the quality of images reconstructed by the BMCR algorithm for motion-contaminated data is (a) significantly superior to that of the MaximumLikelihood Expectation-Maximization (ML-EM) algorithm for motion-contaminate data and (b) even comparable to an MLEM reconstruction for motion-free data.