Title: MCMC approach on Bayesian image analysis in Fourier space
Authors: John Kornak - University of California, San Francisco (United States)
Hernando Ombao - King Abdullah University of Science and Technology (KAUST) (Saudi Arabia)
Konstantinos Bakas - King Abdullah University of Science and Technology (Saudi Arabia) [presenting]
Abstract: 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 will 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 spatially correlated processes in image space can be modeled via independent processes in 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, i.e. providing just a single point estimate. A posterior sampling approach for BIFS is presented 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 and mixing concerns that commonly have to be dealt with in high dimensional Markov Chain Monte Carlo sampling problems are avoided.