Author

Jakub Michel

Date of Graduation

Spring 2013

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Songfeng Zheng

Keywords

Markov Chain Monte Carlo, Bayesian statistics, Gibbs sampling, Ising model, image denoising

Subject Categories

Mathematics

Abstract

Markov chain Monte Carlo in the last few decades has become a very popular class of algorithms for sampling from probability distributions based on constructing a Markov chain. A special case of the Markov chain Monte Carlo is the Gibbs sampling algorithm. This algorithm can be used in such a way that it takes into account the prior distribution and likelihood function, carrying a randomly generated variable through the calculation and the simulation. In this thesis, we use the Ising model for the prior of the binary images. Assuming the pixels in binary images are polluted by random noise, we build a Bayesian model for the posterior distribution of the true image data. The posterior distribution enables us to generate the denoised image by designing a Gibbs sampling algorithm.

Copyright

© Jakub 0 Michel

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