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Tree approximation with anisotropic decompositions

by P. Grohs

(Report number 2010-44)

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.

Keywords:

@Techreport{G10_442,
  author = {P. Grohs},
  title = {Tree approximation with anisotropic decompositions },
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2010-44},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2010/2010-44.pdf },
  year = {2010}
}

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