  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 Ciak, Melching and Scherzer
"Regularization with Metric Double Integrals of Functions with Values in a Set
of Vectors", in: Journal of Mathematical Imaging and Vision (2019), 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.
