  Bayesian image analysis has played a large role over the last 40+ years in
solving problems in image noise-reduction, de-blurring, feature enhancement,
and object detection. However, these problems can be complex and lead to
computational difficulties, due to the modeled interdependence between spatial
locations. The Bayesian image analysis in Fourier space (BIFS) approach
proposed here reformulates the conventional Bayesian image analysis paradigm
for continuous valued images as a large set of independent (but heterogeneous)
processes over Fourier space. The original high-dimensional estimation problem
in image space is thereby broken down into (trivially parallelizable)
independent one-dimensional problems in Fourier space. The BIFS approach leads
to easy model specification with fast and direct computation, a wide range of
possible prior characteristics, easy modeling of isotropy into the prior, and
models that are effectively invariant to changes in image resolution.
