Statistical multiscale ideas have been successfully applied in various areas, mainly in the context of one dimensional density estimation and regression. In this talk we develop this idea for two and three dimensional imaging problems. This leads to new constrained optimization problems where the constraints are given by bounds on the multiresolution norm and we suggest algorithms for this. Furthermore, we discuss some open problems in extreme value theory in connection to our work. Finally, we show how statistical multiscale methods can be used for deconvolution problems. This is applied to subdiffraction fluorescence microscopy for the estimation of protein distributions in cytoskeletons of cells.

Keywords: Statistical inverse problems; Biophotonic imaging; Statistical multiscale; Convex optimization

Biography: Axel Munk is Felix-Bernstein Professor for Mathematical Statistics with the Institute for Mathematical Stochastics, Georg August University Goettingen and fellow of the Max-Planck Institute for Biophysical Chemistry, Goettingen. His main fields of interest are Nonparametric Statistics, Statistical Inverse Problems and Applications in Biophyiscs. Currently he is Associate Editor of four Statistics Journals.