On the self-regularization property of the EM algorithm for Poisson inverse problems

Axel Munk () and Mihaela Pricop ()
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Axel Munk: Institut für Mathematische Stochastik, Georg August Universität Göttingen
Mihaela Pricop: Institut für Mathematische Stochastik, Georg August Universität Göttingen

A chapter in Statistical Modelling and Regression Structures, 2010, pp 431-448 from Springer

Abstract: Abstract One of the most interesting properties of the EM algorithm for image reconstruction from Poisson data is that, if initialized with a uniform image, the first iterations improve the quality of the reconstruction up to a point and it deteriorates later dramatically. This ’self- regularization’ behavior is explained in this article for a very simple noise model.We further study the influence of the scaling of the kernel of the operator involved on the total error of the EM algorithm. This is done in a semi- continuous setting and we compute lower bounds for the L1 risk. Numerical simulations and an example from fluorescence microscopy illustrate these results.

Keywords: Positron Emission Tomography; Inverse Problem; Expectation Maximization; Expectation Maximization Algorithm; Linear Inverse Problem (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2413-1_23

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DOI: 10.1007/978-3-7908-2413-1_23

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