Shearlets on Bounded Domains
Functional Analysis
2010-07-20 v1
Abstract
Shearlet systems have so far been only considered as a means to analyze -functions defined on , which exhibit curvilinear singularities. However, in applications such as image processing or numerical solvers of partial differential equations the function to be analyzed or efficiently encoded is typically defined on a non-rectangular shaped bounded domain. Motivated by these applications, in this paper, we first introduce a novel model for cartoon-like images defined on a bounded domain. We then prove that compactly supported shearlet frames satisfying some weak decay and smoothness conditions, when orthogonally projected onto the bounded domain, do provide (almost) optimally sparse approximations of elements belonging to this model class.
Cite
@article{arxiv.1007.3039,
title = {Shearlets on Bounded Domains},
author = {Gitta Kutyniok and Wang-Q Lim},
journal= {arXiv preprint arXiv:1007.3039},
year = {2010}
}