Jan Modersitzki

Martin Burger, Jan Modersitzki, Sebastian Suhr

The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial density including preservation of mass. Consequently we derive a variational regularization model for the reconstruction, which - besides the usual data fidelity and total variation regularization of the images - also includes a motion constraint and a hyperelastic regularization energy. Under suitable assumptions we prove the existence of a minimizer, which relies on the concept of weak diffeomorphisms for the motion. Moreover, we study natural parameter asymptotics and regularizing properties of the variational model. Finally, we develop a computational solution method based on alternating minimization and splitting techniques, with a particular focus on dynamic PET. The potential improvements of our approach compared to conventional reconstruction techniques are investigated in appropriately designed examples.

Hari Om Aggrawal, Jan Modersitzki

Multilevel strategies are an integral part of many image registration algorithms. These strategies are very well-known for avoiding undesirable local minima, providing an outstanding initial guess, and reducing overall computation time. State-of-the-art multilevel strategies build a hierarchy of discretization in the spatial dimensions. In this paper, we present a spatio-temporal strategy, where we introduce a hierarchical discretization in the temporal dimension at each spatial level. This strategy is suitable for a motion estimation problem where the motion is assumed smooth over time. Our strategy exploits the temporal smoothness among image frames by following a predictor-corrector approach. The strategy predicts the motion by a novel interpolation method and later corrects it by registration. The prediction step provides a good initial guess for the correction step, hence reduces the overall computational time for registration. The acceleration is achieved by a factor of 2.5 on average, over the state-of-the-art multilevel methods on three examined optical coherence tomography datasets.