Abstract
Many problems in digital image processing require the ability to recover missing parts of an image or to remove spurious or undesired objects. One can mention for instance the removal of scratches in old photographs and films, the recovery of pixel blocks corrupted during a binary transmission (or analogously the removal of impulse noise) or the removal of undesired publicity, text or subtitles from a photograph. One can also think of special effects for movie postproduction, e.g. the removal of a microphone appearing in a scene. A digital image is usually modeled as a function u from a bounded domain of R (N = 2 for usual snapshots, N = 3 for medical images or movies, N = 4 for moving medical images) onto R (M = 1 for a grey level image, M = 3 for colour images). Since it is now well admitted that the essential features of any natural image are contained in its grey level representation, we shall concentrate on the panchromatic case M = 1. To extend to the colour case an operator designed for grey level images, it is generally enough to process separately each channel in the colour representation, e.g. the red-green-blue representation or, more appropriately, any representation with
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