ADAPTIVE MULTIRESOLUTION ANALYSIS STRUCTURES AND SHEARLET SYSTEMS
Autor(en): | Han, Bin Kutyniok, Gitta Shen, Zuowei |
Stichwörter: | adaptive multiresolution analysis; AFFINE SYSTEMS; APPROXIMATION; CONTINUOUS CURVELET TRANSFORM; EFFICIENT; fast decomposition algorithm; FRAME; IMAGE; L-2(R-D); Mathematics; Mathematics, Applied; RESOLUTION; shearlets; tight frames; WAVELETS | Erscheinungsdatum: | 2011 | Herausgeber: | SIAM PUBLICATIONS | Journal: | SIAM JOURNAL ON NUMERICAL ANALYSIS | Volumen: | 49 | Ausgabe: | 5 | Startseite: | 1921 | Seitenende: | 1946 | Zusammenfassung: | 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. |
ISSN: | 00361429 | DOI: | 10.1137/090780912 |
Zur Langanzeige
Seitenaufrufe
1
Letzte Woche
0
0
Letzter Monat
0
0
geprüft am 10.05.2024