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Erschienen in:
2013 | OriginalPaper | Buchkapitel
An Optimal Control Approach to Find Sparse Data for Laplace Interpolation
verfasst von : Laurent Hoeltgen, Simon Setzer, Joachim Weickert
Erschienen in: Energy Minimization Methods in Computer Vision and Pattern Recognition
Verlag: Springer Berlin Heidelberg
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Finding optimal data for inpainting is a key problem in the context of partial differential equation-based image compression. We present a new model for optimising the data used for the reconstruction by the underlying homogeneous diffusion process. Our approach is based on an optimal control framework with a strictly convex cost functional containing an
L
1
term to enforce sparsity of the data and non-convex constraints. We propose a numerical approach that solves a series of convex optimisation problems with linear constraints. Our numerical examples show that it outperforms existing methods with respect to quality and computation time.