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EM Algorithms

In: Handbook of Mathematical Methods in Imaging

Author

Listed:
  • Charles Byrne

    (University of Massachusetts Lowell, Department of Mathematical Sciences)

  • Paul P. B. Eggermont

    (University of Delaware, Food and Resource Economics)

Abstract

Expectation-maximization algorithms, or em algorithms for short, are iterative algorithms designed to solve maximum likelihood estimation problems. The general setting is that one observes a random sample Y 1, Y 2, …, Y n of a random variable Y whose probability density function (pdf) f ( ⋅ | x o ) $$f(\,\cdot \,\vert \,x_{o})$$ with respect to some (known) dominating measure is known up to an unknown “parameter” x o . The goal is to estimate x o and, one might add, to do it well. In this chapter, that means to solve the maximum likelihood problem.

Suggested Citation

  • Charles Byrne & Paul P. B. Eggermont, 2015. "EM Algorithms," Springer Books, in: Otmar Scherzer (ed.), Handbook of Mathematical Methods in Imaging, edition 2, pages 305-388, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0790-8_8
    DOI: 10.1007/978-1-4939-0790-8_8
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    Cited by:

    1. Crucinio, Francesca R. & De Bortoli, Valentin & Doucet, Arnaud & Johansen, Adam M., 2024. "Solving a class of Fredholm integral equations of the first kind via Wasserstein gradient flows," Stochastic Processes and their Applications, Elsevier, vol. 173(C).

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