On the self-regularization property of the EM algorithm for Poisson inverse problems
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.
KeywordsPositron Emission Tomography Inverse Problem Expectation Maximization Expectation Maximization Algorithm Linear Inverse Problem
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M. Pricop and A. Munk acknowledge support of DFG SFB 755 and FOR 916.We are grateful to P. Marnitz, A. Esner, S. Mek and A. Schoenle for the 4π images used in the introduction.
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