Adaptive Multiresolution Analysis Structures and Shearlet Systems

Han, Bin; Kutyniok, Gitta und Shen, Zuowei (2011): Adaptive Multiresolution Analysis Structures and Shearlet Systems. In: SIAM Journal on Numerical Analysis, Vol. 49, No. 5: pp. 1921-1946

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0036-1429
• Language: English