Convergence of Variational Regularization Methods for Imaging on   Riemannian Manifolds
  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. 
Nicolas Thorstensen and Otmar Scherzer
math.NA math.OC