An anisotropic directional subdivision and multiresolution scheme

In order to handle directional singularities, standard wavelet approaches have been extended to the concept of discrete shearlets in Kutyniok and Sauer (SIAM J. Math. Anal. 41, 1436–1471, 2009). 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 means of 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 the same amount of data.