Nonlinear Flows for Displacement Correction and Applications in Tomography
In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We show a preliminary convergence result of a relaxed convexification of the non-convex optimization problem. Some properties on the behavior of the solutions of these filtering flows are studied by numerical analysis. At the end, we provide examples for correcting angular perturbations in tomographical data.
KeywordsNon-convex regularization Nonlinear flow Displacement correction Radon transform Angular perturbation
The authors thank the reviewers for some helpful comments. The work of OS has been supported by the Austrian Science Fund (FWF): Geometry and Simulation, project S11704 (Variational methods for imaging on manifolds), and Interdisciplinary Coupled Physics Imaging, project P26687-N25.
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