An MCMC Approach to Bayesian Image Analysis in Fourier Space
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Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A primary limitation of these approaches is the computational complexity due to the interdependence of neighboring pixels which limits the ability to perform full posterior sampling through Markov chain Monte Carlo (MCMC). To alleviate this problem, we develop a new posterior sampling method that is based on modeling the prior and likelihood in the space of the Fourier transform of the image. One advantage of Fourier-based methods is that many spatially correlated processes in image space can be represented via independent processes over Fourier space. A recent approach known as Bayesian Image Analysis in Fourier Space (or BIFS), has introduced parameter functions to describe prior expectations about image properties in Fourier space. To date BIFS has relied on Maximum a Posteriori (MAP) estimation for generating posterior estimates; providing just a single point estimate. The work presented here develops a posterior sampling approach for BIFS that can explore the full posterior distribution while continuing to take advantage of the independence modeling over Fourier space. As a result computational efficiency is improved over that for conventional Bayesian image analysis and mixing concerns that commonly have to be dealt with in high dimensional Markov chain Monte Carlo sampling problems are avoided. Implementation results and details are provided using simulated data.
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