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. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Munk, A., & Pricop, M. (2010). On the self-regularization property of the em algorithm for poisson inverse problems. In Statistical Modelling and Regression Structures: Festschrift in Honour of Ludwig Fahrmeir (pp. 431–448). Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2413-1_23
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