2009/12/22 by Bin Han, Gitta Kutyniok, Han, Bin +3
Computer Science · Engineering · Mathematics · #42C15 #42C40 #65T60 #65T99 #94A08 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.0912.4529
openalex publication_date 2009/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we first introduce the concept of an adaptive MRA (AMRA) structure which is a variant of the classical MRA structure 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 matrices optimally close to rotation as well as 3D shearlet systems are studied within this framework.