An MCMC Approach to Bayesian Image Analysis in Fourier Space

Oregon Convention Center 

Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A limitation of these approaches is the computational complexity due to the interdependence of neighboring pixels which limits the efficiency of performing full posterior sampling through Markov chain Monte Carlo (MCMC). To alleviate this, 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 a large set of 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 the concept of parameter functions to describe prior expectations about distributional parameters over Fourier space. The work presented here extends BIFS to a posterior sampling approach that can explore a range of posterior estimators beyond the MAP estimate. Computational efficiency of MCMC for BIFS is much improved over that for conventional Bayesian image analysis and mixing concerns are avoided.

Bayesian image analysis

Markov chain Monte Carlo 

Section on Statistics in Imaging