Statistical Multiresolution Estimation for Variational Imaging: With an Application in Poisson-Biophotonics
2013 | journal article; research paper. A publication with affiliation to the University of Göttingen.
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Details
- Authors
- Frick, Klaus; Marnitz, Philipp; Munk, Axel
- 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 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.
- Issue Date
- 2013
- Journal
- Journal of Mathematical Imaging and Vision
- Organization
- Fakultät für Mathematik und Informatik
- ISSN
- 0924-9907
- eISSN
- 1573-7683
- Language
- English