Recursive Filter for Defocus Correction on a non-uniform Sample Grid with Stability Control

The article discusses the technology of constructing a recursive filter on a non-uniform grid of samples with the parameters identification on test images. This filter is the IIR-filter that has a physical feasibility problem. To over-come it, a multi-step procedure is implemented. Unfortunately, identifying the best filter in terms of a given criterion does not guarantee that a recursive implementation of that filter will be stable. In the paper, for the considered iterative scheme, stability conditions are obtained. It has been experimentally confirmed that if these conditions are met, it is possible to achieve a high quality of correction. Based on the obtained criteria, a technology for correcting defocusing with control over the stability of estimates is proposed. The results of image correction showing the effectiveness of the technology are presented.