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Author: Papafitsoros, Kostas × End date: 2024 × Start date: 2021 × End date: 2024 × Start date: 2020 × DDC: 510 × Type: article × WGL Institute: WIAS ×

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    Variable Step Mollifiers and Applications
    (Berlin ; Heidelberg : Springer, 2020) Hintermüller, Michael; Papafitsoros, Kostas; Rautenberg, Carlos N.
    We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of the operator in all basic Lebesgue, Sobolev and BV spaces as well as corresponding approximation results. The results are then applied to extend recently developed theory concerning the density of convex intersections. © 2020, The Author(s).
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    Patch-Wise Adaptive Weights Smoothing in R
    (Los Angeles, Calif. : UCLA, Dept. of Statistics, 2020) Polzehl, Jörg; Papafitsoros, Kostas; Tabelow, Karsten
    Image reconstruction from noisy data has a long history of methodological development and is based on a variety of ideas. In this paper we introduce a new method called patch-wise adaptive smoothing, that extends the propagation-separation approach by using comparisons of local patches of image intensities to define local adaptive weighting schemes for an improved balance of reduced variability and bias in the reconstruction result. We present the implementation of the new method in an R package aws and demonstrate its properties on a number of examples in comparison with other state-of-the art image reconstruction methods. © 2020, American Statistical Association. All rights reserved.