ORCID: https://orcid.org/0000-0001-9738-2487 und Shen, Zuowei
(2011):
Adaptive Multiresolution Analysis Structures and Shearlet Systems.
In: SIAM Journal on Numerical Analysis, Bd. 49, Nr. 5: S. 1921-1946
Abstract
In this paper, we first introduce the concept of an adaptive multiresolution analysis (AMRA) structure, which is a variant of the classical MRA structure well suited to the main goal of a fast flexible decomposition strategy adapted to the data at each decomposition level. We then study this novel methodology for the general case of affine-like systems and derive a unitary extension principle (UEP) for filter design. Finally, we apply our results to the directional representation system of shearlets. This leads to a comprehensive theory for fast decomposition algorithms associated with shearlet systems which encompasses tight shearlet frames with spatially compactly supported generators within such an AMRA structure. Also, shearlet-like systems associated with parabolic scaling and unimodular shear matrices are studied within this framework.
Dokumententyp: | Zeitschriftenartikel |
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Fakultät: | Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz |
Themengebiete: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
ISSN: | 0036-1429 |
Sprache: | Englisch |
Dokumenten ID: | 126444 |
Datum der Veröffentlichung auf Open Access LMU: | 27. Mai 2025 06:07 |
Letzte Änderungen: | 27. Mai 2025 06:07 |