An anisotropic directional multiresolution and subdivision scheme

In order to handle directional singularities, standard wavelet approaches have been extended to the concept of discrete shearlets in [9]. One disadvantage of this extension, however, is the relatively large determinant of the scaling matrices used there which results in a substantial data complexity. This motivates the question whether some of the features of the discrete shearlets can also be obtained by meansof different geometries.In this paper, we give a positive answer by presenting a different approach, based on a matrix with small determinant which therefore offers a larger recursion depth for thesame amount of data.