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.

Cotronei, M., Ghisi, D., Rossini, M., & Sauer, T. (2015). An anisotropic directional subdivision and multiresolution scheme. ADVANCES IN COMPUTATIONAL MATHEMATICS, 41(3), 709-726 [10.1007/s10444-014-9384-x].

An anisotropic directional subdivision and multiresolution scheme

ROSSINI, MILVIA FRANCESCA;
2015

Abstract

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.
Si
Articolo in rivista - Articolo scientifico
Scientifica
Filterbank; Multiple multiresolution analysis; Subdivision;
Filterbank; Multiple multiresolution analysis; Subdivision; Applied Mathematics; Computational Mathematics
English
709
726
18
Cotronei, M., Ghisi, D., Rossini, M., & Sauer, T. (2015). An anisotropic directional subdivision and multiresolution scheme. ADVANCES IN COMPUTATIONAL MATHEMATICS, 41(3), 709-726 [10.1007/s10444-014-9384-x].
Cotronei, M; Ghisi, D; Rossini, M; Sauer, T
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/98738
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