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|Title:||Adaptive multiresolution analysis structures and shearlet systems|
|Keywords:||Adaptive multiresolution analysis|
Fast decomposition algorithm
|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|
|Appears in Collections:||Staff Publications|
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