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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 |
Appears in Collections: | Staff Publications |
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