**Up:** Abstract

A&A Supplement Ser., Vol. 124, July 1997, 197-203

Received February 28, 1995; accepted September 1, 1996

## Image restoration by simple adaptive deconvolution

**W. Waniak**

Astronomical Observatory of the Jagiellonian University,
ul. Orla 171, 30-244 Kraków, Poland

### Abstract:

A new version of an iterative scheme of deconvolution originally introduced by
Richardson (1972) and Lucy (1974) is presented. This algorithm is based on the
Maximum Likelihood principle and imposes additional constraints on the solution
of the inverse problem. The main idea of the newly presented method is to link
the number of Richardson-Lucy iterations with the local difference between the
object profile in the input image and the noisy background. If this difference
is of the order of the 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. Thus, the number of iterations
is used as a regularizer for the restoration. Due to this adaptive approach,
the background noise is highly suppressed and the probability of restoration
artefacts is seriously diminished. What is more, the quality of restored images
(described by the Kullback-Leibler distance between deconvolved and original
profile) for the adaptive iterative scheme increases in comparison with the
original approach, whereas the mean number of iterations per one pixel is
substantially reduced. Some examples of the deconvolution of one- and
two-dimensional profiles presenting advantages of the new algorithm are
described. Photometric fidelity of both methods is also compared and the
predominance of the adaptive approach is confirmed.

**keywords:** methods: data analysis -- techniques: image processing

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