A convexity based method for approximation and interpolation of sampled functions

      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 for a given continuous or Lipschitz function.  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.