Image restoration by simple adaptive deconvolution

Abstract

A new version of an iterative scheme of de-convolution 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 regular-izer 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.