M. Blume, M. Rafecas, S. I. Ziegler, N. Navab Combined Motion Compensation and Reconstruction for PET Proc. IEEE Nuclear Science Symposium and Medical Imaging Conference, Dresden, Germany, October 2008 (bib)
	A major limitation of high-resolution positron-emission-tomography (PET) is subject movements during acquisition. In the last decade, many methods for dealing with motion have been proposed. They can be roughly divided into two categories: Those which try to get the motion data from the data (intrinsic), and those that use additional methods like optical tracking to acquire the motion information (extrinsic). We propose a new intrinsic algorithm called "Blind Motion Compensated Reconstruction" (BMCR) that is able to deal with 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. This framework 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. We believe that such a combined framework can overcome problems of existing intrinsic 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. We aim at filling this gap with our combined framework for registration and reconstruction. 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 Maximum-Likelihood Expectation-Maximization (ML-EM) algorithm for motion-contaminated data and (b) even comparable to an ML-EM reconstruction for motion-free data.
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