3,189 research outputs found
Total variation regularization for manifold-valued data
We consider total variation minimization for manifold valued data. We propose
a cyclic proximal point algorithm and a parallel proximal point algorithm to
minimize TV functionals with -type data terms in the manifold case.
These algorithms are based on iterative geodesic averaging which makes them
easily applicable to a large class of data manifolds. As an application, we
consider denoising images which take their values in a manifold. We apply our
algorithms to diffusion tensor images, interferometric SAR images as well as
sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds
(which includes the data space in diffusion tensor imaging) we show the
convergence of the proposed TV minimizing algorithms to a global minimizer
Total variation regularization of multi-material topology optimization
This work is concerned with the determination of the diffusion coefficient
from distributed data of the state. This problem is related to homogenization
theory on the one hand and to regularization theory on the other hand. An
approach is proposed which involves total variation regularization combined
with a suitably chosen cost functional that promotes the diffusion coefficient
assuming prespecified values at each point of the domain. The main difficulty
lies in the delicate functional-analytic structure of the resulting
nondifferentiable optimization problem with pointwise constraints for functions
of bounded variation, which makes the derivation of useful pointwise optimality
conditions challenging. To cope with this difficulty, a novel reparametrization
technique is introduced. Numerical examples using a regularized semismooth
Newton method illustrate the structure of the obtained diffusion coefficient.
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