Advances in Computational Mathematics

, Volume 41, Issue 3, pp 709–726

An anisotropic directional subdivision and multiresolution scheme

  • Mariantonia Cotronei
  • Daniele Ghisi
  • Milvia Rossini
  • Tomas Sauer
Article

DOI: 10.1007/s10444-014-9384-x

Cite this article as:
Cotronei, M., Ghisi, D., Rossini, M. et al. Adv Comput Math (2015) 41: 709. doi:10.1007/s10444-014-9384-x

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.

Keywords

Subdivision Filterbank Multiple multiresolution analysis 

Mathematics Subject Classification (2000)

65T60 41A05 42C15 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Mariantonia Cotronei
    • 1
  • Daniele Ghisi
    • 2
  • Milvia Rossini
    • 2
  • Tomas Sauer
    • 3
  1. 1.DIIESUniversità Mediterranea di Reggio CalabriaReggio CalabriaItaly
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità degli Studi di Milano-BicoccaMilanoItaly
  3. 3.Lehrstuhl für Mathematik mit Schwerpunkt Digitale SignalverarbeitungUniversität PassauPassauGermany

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