A Unitary Extension Principle for Shearlet Systems - Mathematics > Numerical AnalysisReport as inadecuate




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Abstract: In this paper, we first introduce the concept of an adaptive MRA AMRAstructure which is a variant of the classical MRA structure suited to the maingoal of a fast flexible decomposition strategy adapted to the data at eachdecomposition level. We then study this novel methodology for the general caseof affine-like systems, and derive a Unitary Extension Principle UEP forfilter design. Finally, we apply our results to the directional representationsystem of shearlets. This leads to a comprehensive theory for fastdecomposition algorithms associated with shearlet systems which encompassestight shearlet frames with spatially compactly supported generators within suchan AMRA structure. Also shearlet-like systems associated with parabolic scalingand unimodular matrices optimally close to rotation as well as 3D shearletsystems are studied within this framework.



Author: Bin Han, Gitta Kutyniok, Zuowei Shen

Source: https://arxiv.org/







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