Regularization with metric double integrals for vector tomography-Reference-Cited by-同舟云学术

Regularization with metric double integrals for vector tomography

Published:2020-09-01 Issue:6 Volume:28 Page:857-875
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Melching Melanie¹^ORCID,Scherzer Otmar²^ORCID

Affiliation:

1. Faculty of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1, A-1090 Vienna , Austria

2. Faculty of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1, A-1090 Vienna ; and Johann Radon Institute for Computational and Applied Mathematics (RICAM), Altenbergerstraße 69, A-4040 Linz , Austria

Abstract

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 [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.

Funder

Austrian Science Fund

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2019-0084/pdf

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