Frick, KlausKlausFrickMarnitz, PhilippPhilippMarnitzMunk, AxelAxelMunk2017-09-072017-09-072013https://resolver.sub.uni-goettingen.de/purl?gro-2/7153In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in Frick et al. (Electron. J. Stat. 6:231-268, 2012). It constitutes a variational regularization technique that uses an a"" (a)-type distance measure as data-fidelity combined with a convex cost functional. The resulting convex optimization problem is approached by a combination of an inexact alternating direction method of multipliers and Dykstra's projection algorithm. We describe a novel method for balancing data-fit and regularity that is fully automatic and allows for a sound statistical interpretation. The performance of our estimation approach is studied for various problems in imaging. Among others, this includes deconvolution problems that arise in Poisson nanoscale fluorescence microscopy.enGoescholarhttps://goescholar.uni-goettingen.de/licensejournal_article10.1007/s10851-012-0368-50003202808000063142336https://resolver.sub.uni-goettingen.de/purl?gs-1/10359