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Convergence of Variational Regularization Methods for Imaging on Riemannian Manifolds | | Nicolas Thorstensen
; Otmar Scherzer
; | | Date: |
12 May 2011 | | 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. | | Source: | arXiv, 1105.2407 | | Services: | Forum | Review | PDF | Favorites | |
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