Anzeige
Erschienen in:
2012 | OriginalPaper | Buchkapitel
Shearlets on Bounded Domains
verfasst von : Gitta Kutyniok, Wang-Q Lim
Erschienen in: Approximation Theory XIII: San Antonio 2010
Verlag: Springer New York
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Shearlet systems have so far been only considered as a means to analyze
L
2
-functions defined on
$${\mathbb{R}}^{2}$$
, 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.