ORCID: https://orcid.org/0000-0001-9738-2487 und Lim, Wang-Q
(2011):
Compactly supported shearlets are optimally sparse.
In: Journal of Approximation Theory, Bd. 163, Nr. 11: S. 1564-1589
Abstract
Cartoon-like images, i.e., C2 functions which are smooth apart from a C2 dis- continuity curve, have by now become a standard model for measuring sparse (non-linear) approximation properties of directional representation systems. It was already shown that curvelets, contourlets, as well as shearlets do ex- hibit (almost) optimally sparse approximations within this model. However, all those results are only applicable to band-limited generators, whereas, in particular, spatially compactly supported generators are of uttermost impor- tance for applications.
In this paper, we now present the first complete proof of (almost) op- timally sparse approximations of cartoon-like images by using a particular class of directional representation systems, which indeed consists of com- pactly supported elements. This class will be chosen as a subset of shearlet frames – not necessarily required to be tight – with shearlet generators having compact support and satisfying some weak moment conditions.
Dokumententyp: | Zeitschriftenartikel |
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Keywords: | Curvilinear discontinuities; edges; nonlinear approximation; optimal sparsity; shearlets; thresholding; wavelets |
Fakultät: | Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz |
Themengebiete: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
ISSN: | 00219045 |
Sprache: | Englisch |
Dokumenten ID: | 126443 |
Datum der Veröffentlichung auf Open Access LMU: | 27. Mai 2025 06:09 |
Letzte Änderungen: | 27. Mai 2025 06:09 |