  Bayesian image restoration has had a long history of successful application
but one of the limitations that has prevented more widespread use is that the
methods are generally computationally intensive. The authors recently addressed
this issue by developing a method that performs the image enhancement in an
orthogonal space (Fourier space in that case) which effectively transforms the
problem from a large multivariate optimization problem to a set of smaller
independent univariate optimization problems. The current paper extends these
methods to analysis in another orthogonal basis, wavelets. While still
providing the computational efficiency obtained with the original method in
Fourier space, this extension allows more flexibility in adapting to local
properties of the images, as well as capitalizing on the long history of
developments for wavelet shrinkage methods. In addition, wavelet methods,
including empirical Bayes specific methods, have recently been developed to
effectively capture multifractal properties of images. An extension of these
methods is utilized to enhance the recovery of textural characteristics of the
underlying image. These enhancements should be beneficial in characterizing
textural differences such as those occurring in medical images of diseased and
healthy tissues. The Bayesian framework defined in the space of wavelets
provides a flexible model that is easily extended to a variety of imaging
contexts.
