期刊
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
卷 46, 期 2, 页码 384-399出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2017.06.002
关键词
Shearlets; Curvature; Compactly supported generator
资金
- ERC [ERC-2010-StG 259550]
- DFG Collaborative Research Center Discretization in Geometry and Dynamics [TRR 109]
- Berlin Mathematical School
We introduce bendlets, a shearlet-like system that is based on anisotropic scaling, translation, shearing, and bending of a compactly supported generator. With shearing being linear and bending quadratic in spatial coordinates, bendlets provide what we term a second-order shearlet system. As we show in this article, the decay rates of the associated transform enable the precise characterization of location, orientation and curvature of discontinuities in piecewise constant images. These results yield an improvement over existing directional representation systems where curvature only controls the constant of the decay rate of the transform. We also detail the construction of shearlet systems of arbitrary order. A practical implementation of bendlets is provided as an extension of the ShearLab toolbox, which we use to verify our theoretical classification results. (C) 2017 Elsevier Inc. All rights reserved.
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