Regularization with metric double integrals for vector tomography

We present a family of non-local variational regularization methods for solving tomographic problems, where the solutions are functions with range in a closed subset of the Euclidean space, for example if the solution only attains values in an embedded sub-manifold. Recently, in [R. Ciak, M. Melching and O. Scherzer, Regularization with metric double integrals of functions with values in a set of vectors, J. Math. Imaging Vision 61 2019, 6, 824–848], such regularization methods have been investigated analytically and their efficiency has been tested for basic imaging tasks such as denoising and inpainting. In this paper we investigate solving complex vector tomography problems with non-local variational methods both analytically and numerically.