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Tree approximation with anisotropic decompositions
- Source :
-
Applied & Computational Harmonic Analysis . Jul2012, Vol. 33 Issue 1, p44-57. 14p. - Publication Year :
- 2012
-
Abstract
- Abstract: In recent years anisotropic transforms like the shearlet or curvelet transform have received a considerable amount of interest due to their ability to efficiently capture anisotropic features in terms of nonlinear N-term approximation. In this paper we study tree-approximation properties of such transforms where the N-term approximant has to satisfy the additional constraint that the set of kept indices possesses a tree structure. The main result of this paper is that for shearlet- and related systems, this additional constraint does not deteriorate the approximation rate. As an application of our results we construct (almost) optimal encoding schemes for cartoon images. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 10635203
- Volume :
- 33
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Applied & Computational Harmonic Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 74639905
- Full Text :
- https://doi.org/10.1016/j.acha.2011.09.004