Non-monotonic Poisson Likelihood Maximization

Sra, S; Kim, D; Schölkopf, B

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Non-monotonic Poisson Likelihood Maximization

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Sra, S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schölkopf, B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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MPIK-TR-170.pdf
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Sra, S., Kim, D., & Schölkopf, B.(2008). Non-monotonic Poisson Likelihood Maximization (170). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-C90D-0

Abstract

This report summarizes the theory and some main applications of a new non-monotonic algorithm for
maximizing a Poisson Likelihood, which for Positron Emission Tomography (PET) is equivalent to minimizing
the associated Kullback-Leibler Divergence, and for Transmission Tomography is similar to maximizing the dual
of a maximum entropy problem. We call our method non-monotonic maximum likelihood (NMML) and show
its application to different problems such as tomography and image restoration. We discuss some theoretical
properties such as convergence for our algorithm. Our experimental results indicate that speedups obtained via our
non-monotonic methods are substantial.