An MCMC Approach to Bayesian Image Analysis in Fourier Space - Konstantinos Bakas; John Kornak; Hernando Ombao (Data Science in Science)
Bayesian image analysis methods are commonly applied to solve image analysis problems such as noise reduction, feature enhancement, and object detection. A primary limitation of these methods is their computational cost due to the complex joint interdependencies between pixels, which limits the efficiency of performing posterior sampling through Markov chain Monte Carlo (MCMC). To alleviate this problem, we develop a new posterior sampling method 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, Bayesian Image Analysis in Fourier Space (BIFS), introduced parameter functions to describe prior expectations about distributional parameters over Fourier space. To date, BIFS has relied on Maximum a Posteriori (MAP) estimation. This work extends BIFS to an MCMC approach, allowing a range of posterior estimators, including credible intervals and posterior probability maps. The computational efficiency of MCMC for BIFS is much improved over conventional Bayesian image analysis, and mixing concerns that are ubiquitous in high-dimensional MCMC sampling problems are avoided.