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arXiv · 1105.2407

Convergence of Variational Regularization Methods for Imaging on Riemannian Manifolds

Nicolas Thorstensen·Otmar Scherzer
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Abstract

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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Nicolas Thorstensen, Otmar Scherzer. 2011-05-12. Convergence of Variational Regularization Methods for Imaging on Riemannian Manifolds. https://doi.org/10.1088/0266-5611%2F28%2F1%2F015007

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