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

Frick, K.; Marnitz, P.; Munk, A.

doi:10.1007/s10851-012-0368-5

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

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Munk, A.
Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society;

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Citation

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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-FD22-3

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.