A major problem of high-resolution positron-emission-tomography (PET) are subject movements during acquisition. We propose a new motion compensation algorithm called "Blind Motion-Compensated Reconstruction" (BMCR) that is able to deal with frames of extremely low statistics in the case of smooth motion. Our algorithm reconstructs both image and rigid motion just from the recorded data and does not need any external motion tracking.
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 difference 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.
Such a combined framework can overcome problems of existing algorithms which separate reconstruction and motion compensation.
These algorithms usually try to get the motion information by registering reconstructed frames one to each other (in image space).
Their main drawback is that the registration step is likely to be of low accuracy or even fail completely for low-statistics frames.
A quantitative and visual comparison suggests that BMCR is superior to state-of-the-art intrinsic methods.