Regularization with Metric Double Integrals for Vector Tomography

TL;DR

This paper introduces non-local variational regularization techniques using metric double integrals to improve the solution of complex vector tomography problems, extending previous work on denoising and inpainting.

Contribution

It develops new non-local regularization methods specifically tailored for vector tomography, combining analytical and numerical approaches.

Findings

Effective regularization for vector tomography demonstrated

Improved accuracy in complex imaging tasks shown

Theoretical analysis supports numerical results

Abstract

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.