## Local Smoothing Methods in Image Processing

• In this article a new data-adaptive method for smoothing of bivariate functions is developed. The smoothing is done by kernel regression with rotational invariant bivariate kernels. Two or three local bandwidth parameters are chosen automatically by a two-step plug-in approach. The algorithm starts with small global bandwidth parameters, which adapt during a few iterations to the noisy image. In the next step local bandwidths are estimated. Some general asymptotic results about Gasser-Müller-estimators and optimal bandwidth selection are given. The derived local bandwidth estimators converge and are asymptotically normal.

Author: Vera Friederichs urn:nbn:de:hbz:386-kluedo-14990 Report in Wirtschaftsmathematik (WIMA Report) (110) Preprint English 2007 2007 Technische Universität Kaiserslautern 2-d kernel regression; data-adaptive bandwidth choice; iterative bandwidth choice; local bandwidths Fachbereich Mathematik 510 Mathematik

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