Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces
Numerical Analysis
2016-12-15 v2 Differential Geometry
Functional Analysis
Optimization and Control
Abstract
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account perturbations of the surfaces, in particular when the surfaces are approximated by spline surfaces. Another contribution is that we highlight the analysis of regularization for functions with range in vector bundles over surfaces. We also present some practical applications, such as an inverse problem of gravimetry and an imaging problem for denoising vector fields on surfaces, and show the numerical verification.
Cite
@article{arxiv.1510.07028,
title = {Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces},
author = {Guozhi Dong and Bert Juettler and Otmar Scherzer and Thomas Takacs},
journal= {arXiv preprint arXiv:1510.07028},
year = {2016}
}
Comments
31pages