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An Optimal Control Approach to Find Sparse Data for Laplace Interpolation

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Part of the Lecture Notes in Computer Science book series (LNIP,volume 8081)

Abstract

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.

Keywords

  • Laplace Interpolation
  • Optimal Control
  • Inpainting
  • Non-convex Optimisation

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Hoeltgen, L., Setzer, S., Weickert, J. (2013). An Optimal Control Approach to Find Sparse Data for Laplace Interpolation. In: Heyden, A., Kahl, F., Olsson, C., Oskarsson, M., Tai, XC. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2013. Lecture Notes in Computer Science, vol 8081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40395-8_12

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  • DOI: https://doi.org/10.1007/978-3-642-40395-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40394-1

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