  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.
