Statistical Multiresolution Estimation for Variational Imaging: With an Application in Poisson-Biophotonics |
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Authors: | Klaus Frick Philipp Marnitz Axel Munk |
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Affiliation: | 1. Institute for Mathematical Stochastics, University of G?ttingen, Goldschmidtstra?e 7, 37077, G?ttingen, Germany 2. Max Planck Institute for Biophysical Chemistry, Am Fa?berg 11, 37077, G?ttingen, Germany
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Abstract: | In 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 ? ∞-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. |
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