Please use this identifier to cite or link to this item: https://doi.org/10.1137/090780912
Title: Adaptive multiresolution analysis structures and shearlet systems
Authors: Han, B.
Kutyniok, G.
Shen, Z. 
Keywords: Adaptive multiresolution analysis
Affine systems
Fast decomposition algorithm
Shearlets
Tight frames
Issue Date: 2011
Citation: Han, B., Kutyniok, G., Shen, Z. (2011). Adaptive multiresolution analysis structures and shearlet systems. SIAM Journal on Numerical Analysis 49 (5) : 1921-1946. ScholarBank@NUS Repository. https://doi.org/10.1137/090780912
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. © 2011 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Numerical Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/102791
ISSN: 00361429
DOI: 10.1137/090780912
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