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  Statistical multiresolution estimation for variational imaging: With an application in poisson-biophotonics.

Frick, K., Marnitz, P., & Munk, A. (2013). Statistical multiresolution estimation for variational imaging: With an application in poisson-biophotonics. Journal of Mathematical Imaging and Vision, 46(3), 370-387. doi:10.1007/s10851-012-0368-5.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-FD22-3 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0027-CA54-B
Genre: Journal Article

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Frick, K., Author
Marnitz, P., Author
Munk, A.1, Author              
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1Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society, ou_1113580              

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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 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.

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Language(s): eng - English
 Dates: 2012-07-182013-07
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: DOI: 10.1007/s10851-012-0368-5
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Title: Journal of Mathematical Imaging and Vision
Source Genre: Journal
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Publ. Info: Dordrecht, Holland : Kluwer Academic Publishers
Pages: - Volume / Issue: 46 (3) Sequence Number: - Start / End Page: 370 - 387 Identifier: ISSN: 0924-9907
CoNE: /journals/resource/954925566730