Date of Graduation
Spring 2013
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Songfeng Zheng
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.
Keywords
Markov Chain Monte Carlo, Bayesian statistics, Gibbs sampling, Ising model, image denoising
Subject Categories
Mathematics
Copyright
© Jakub 0 Michel
Recommended Citation
Michel, Jakub, "Markov Chain Monte Carlo With Application to Image Denoising" (2013). MSU Graduate Theses. 1649.
https://bearworks.missouristate.edu/theses/1649
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