Variational Methods in Image Restoration

Introduction Optimization has been playing a prominent role in any of the modern image processing techniques, and variational models are used in such different fields as image segmentation and edge detection, compression, and sharpening of blurred images or in noise reduction. The present paper is mainly concerned with the restoration problem, which arises when images have been severely degraded during recording. Restoring a blurred image may be a crucial part of a successful processing when sharp contrasts have been smoothed away by the recording channel. As a consequence, sharpening has to be achieved before other techniques like segmentation, edge detection, or noise suppression could hopefully be brought into play. One of the basic approaches towards enhancing degraded images is by direct filtering, and there exists a vast field of recipes, mostly heuristic, for designing such filters, cf. Jahne [14]. The overall advantage of these direct methods is their computational sp