Ondelettes géométriques adaptatives : vers une utilisation de la distance géodésique
Lebrun, Guillaume · HAL (Le Centre pour la Communication Scientifique Directe) · 2009
Wavelets transform has been introduces last years in the domain of multimedia data processing because they enable a sparse information representation. This transform initially conceived for one dimensional signals, do not use two dimensional signal's specificities. In order to take into account these specificities, several geometrical wavelets transforms have been proposed : two propositions are studied in this thesis. More particularly, we introduce two adaptive geometrical wavelets transforms, i.e., two geometrical wavelets transforms which analysis and synthesis functions are defined once singularities of the image are identified. First transform, defined by Le Pennec, is based on the detection of edges of the image to extract and process separately strips of the image. The second transform is based on a set of measures of geodesic distance specific to the treated signal. This set is then used in a weighted lifting scheme. Both transform are confronted to the suppression of noise and to the suppression of block effect due to JPEG compression. We will comment these results in order to emphasize gains and limits of both approaches.