Décompositions multi-échelles de données définies sur des graphes
Moncef Hidane · HAL (Le Centre pour la Communication Scientifique Directe) · 2013
signals defined on general weighted graphs. This manuscript discusses three approachesthat we have developed.The first approach is based on a variational and iterative process. It generalizes thestructure-texture decomposition, originally proposed for images. Two versions are proposed:one is based on a quadratic prior while the other is based on a total variation prior. Thestudy of the convergence is performed and the choice of parameters discussed in each case.We describe the application of the decompositions we get to the enhancement of details inimages and 3D models.The second approach provides a multiresolution analysis of the space of signals on agiven graph. This construction is based on the organization of the graph as a hierarchy ofpartitions. We have developed an adaptive algorithm for the construction of such hierarchies.Finally, in the third approach, we adapt the lifting scheme to signals on graphs. Thisadaptation raises a number of practical problems. We focused on the one hand on thesubsampling step for which we adopted a greedy approach, and on the other hand on theiteration of the transform on induced subgraphs.