题目：Large Diffeomorphic Deformation Based Image Reconstruction Method for Spatiotemporal Imaging

摘要：We propose a new image reconstruction model for spatiotemporal imaging in large deformation diffeomorphic metric mapping framework. This model can be divided into two subproblems, where one is the usually static image reconstruction, and the other is the so-called indirect image registration. The indirect image registration is one of the significant problems for the image reconstruction in spatiotemporal medical imaging. We adapt the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting, where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends to zero, so it becomes a well-defined regularization method. Moreover, an efficiently computational method is also presented. The talk concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data and the potential extension to spatiotemporal medical imaging.