Image restoration by simple fast adaptive Bayesian deconvolution
Waclaw Waniak
Astronomical Observatory, Jagiellonian University, ul. Orla
171, Krakow, Poland
A new version of Bayesian deconvolution originally introduced
by Lucy (1974) is presented. This algorithm is consistent with
the Maximum Likelihood principle and imposes additional constraints
on the solution of inverse problem. The main characteristic of
the newly presented method is subjection of a number of Lucy iterations
to the local difference between the object profile and the noisy
background. If this difference is of the order of noise level,
only very few iterations are performed, whereas if this difference
is much greater than this level the number of iterations attains
its maximum assigned value. Due to this adaptive approach, the
background noise is highly suppressed and the probability of restoration
artefacts is seriously diminished. What is more, the deconvolving
ability (described by the Kullback-Leibler distance between deconvolved
and original profile) of the adaptive iteration scheme increases
in comparison with the original approach, whereas the mean number
of iterations per one pixel may be substantially less than the
maximum assigned value. Some examples of deconvolution of one-
and two-dimensional profiles presenting advantages of the new
algorithm are described.