<title>Restoration of blurred images by edge detection</title>

Abstract

We present a restoration algorithm using a stable deconvolution for the real images with which we are confronted in our laboratory. In this images, the edge smoothness due to the lack of focusing is not homogeneous. The parameters of the algorithm are determined by the merging of multiscale edge detection. The edge detection is based on a generalization of the Canny-Deriche filter. This filter is used to generate a tight frame of wavelets. We propose a new criterium, the separating power, which allows to choose in a deterministic way the intrinsic parameters of the filters. This criterium introduces the concept of detection resolution which is a new concept in edge detection. Also, we evaluate the maximal delocalization obtained at the limit of the separating power. The merging algorithm is based on human vision which zooms back and forth on the image in order to identify global structures or details in the image. The merging method can be followed by a segmentation method selected from existing ones thus enabling a great adaptability of the complete system in the edge sense. The binary edge representation obtained selects the zones of restoration. Examples of result are presented.