Joint reconstruction of image and motion for PET: Displacement fields versus a B-spline motion model

Joint reconstruction methods of image and motion for Emission Tomography have emerged recently. These methods usually consist in optimizing an objective function which measures the similarity of an estimated data vector to the measured one according to the given estimates for image and motion. Since image reconstruction in ET is dealing with highly noisy data, a robust motion model together with an effective regularization scheme is necessary. In this paper, we compare two joint reconstruction methods which differ in the used motion model: a displacement field model (JRDF) and a B-spline model (JRBS). In the quantitative analysis, JRBS provides a higher maximal correlation coefficient (MCC) than JRDF. Additionally, the MCC of JRBS is located at a lower noise level. These quantitative results are confirmed by a visual comparison, in which JRBS provides straighter edges and a smoother displacement field. We conclude that the B-spline motion model is promising to provide better robustness against noise.