Convergence of Variational Regularization Methods for Imaging on Riemannian Manifolds

Details Convergence of Variational Regularization Methods for Imaging on Riemannian Manifolds Convergence of Variational Regularization Methods for Imaging on Riemannian Manifolds

2011-05-12

arxiv.org/abs/1105.2407v1

Mathematics

Numerical Analysis

Scientific paper

We consider abstract operator equations $Fu=y$, where $F$ is a compact linear operator between Hilbert spaces $U$ and $V$, which are function spaces on \emph{closed, finite dimensional Riemannian manifolds}, respectively. This setting is of interest in numerous applications such as Computer Vision and non-destructive evaluation. In this work, we study the approximation of the solution of the ill-posed operator equation with Tikhonov type regularization methods. We prove well-posedness, stability, convergence, and convergence rates of the regularization methods. Moreover, we study in detail the numerical analysis and the numerical implementation. Finally, we provide for three different inverse problems numerical experiments.

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