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A convexity based method for approximation and interpolation of sampled functions

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VMV - Variational methods and effective algorithms for imaging and vision

 I will briefly introduce the notions of compensated convex transforms and their basic properties. We apply these transforms to define devices for approximating and interpolating sampled functions in Euclidean spaces. I will describe the Huasdorff stability property against samples and the error estimates for inpainting  given continuous or Lipschitz functions.  Prototype examples will also be presented and numerical experiments on applications to salt & pepper noise reduction, the level set reconstruction and image inpainting will also be illustrated. This is a joint work with Elaine Crooks and Antonio Orlando.



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