Bayesian multiscale analysis of images modeled as Gaussian Markov random fields

Authors:
Kevin Thon;HåVard Rue;Stein Olav SkrøVseth;Fred Godtliebsen
Affiliations:
Norwegian Centre for Integrated Care and Telemedicine, University Hospital of North Norway, P.O. Box 6060, N-9038 Tromsø, Norway;Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;Norwegian Centre for Integrated Care and Telemedicine, University Hospital of North Norway, P.O. Box 6060, N-9038 Tromsø, Norway;Department of Mathematics and Statistics, University of Tromsø, N-9037 Tromsø, Norway
Venue:
Computational Statistics & Data Analysis
Year:
2012

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Abstract

A Bayesian multiscale technique for the detection of statistically significant features in noisy images is proposed. The prior is defined as a stationary intrinsic Gaussian Markov random field on a toroidal graph, which enables efficient computation of the relevant posterior marginals. Hence the method is applicable to large images produced by modern digital cameras. The technique is demonstrated in two examples from medical imaging.