Continuous shearlet frames and resolution of the wavefront set
Continuous shearlet frames and resolution of the wavefront set
复制标题
连续剪切波帧和波前集的分辨率
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
P. Grohs
中科院分区：
文献类型：
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作者：
P. Grohs
近年来，像Curvelet-或Shearlet变换这样的定向多尺度变换得到了相当大的关注。这样做的原因是，与小波等更传统的变换不同，这些变换能够有效地处理具有边缘特征的数据。在Kutyniok和Labate(Trans.上午好。数学课。SoC。361：2719-2754,2009)证实了这一性质是由于Kutyniok和Labate，他们证明了对于非常特殊的函数ψ，在紧致锥形波中具有频率支撑的非常特殊的函数ψ关于Shearlet的回火分布f的Shearlet系数的衰减率可以分辨出f的波前集。我们证明了在ψ上更弱的假设下也可以得到相同的结果，即具有足够多的各向异性消失矩。我们还展示了如何从任何这样的函数为$${L^2(mathbb{R}^2)}$$构建框架。为了证明我们的结论，我们开发了一种新的方法，该方法基于Radon变换对剪切波结构的适应。
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are—unlike more traditional transforms like wavelets—able to efficiently handle data with features along edges. The main result in Kutyniok and Labate (Trans. Am. Math. Soc. 361:2719–2754, 2009) confirming this property for shearlets is due to Kutyniok and Labate where it is shown that for very special functions ψ with frequency support in a compact conical wegde the decay rate of the shearlet coefficients of a tempered distribution f with respect to the shearlet ψ can resolve the wavefront set of f. We demonstrate that the same result can be verified under much weaker assumptions on ψ, namely to possess sufficiently many anisotropic vanishing moments. We also show how to build frames for $${L^2(mathbb{R}^2)}$$ from any such function. To prove our statements we develop a new approach based on an adaption of the Radon transform to the shearlet structure.
影响因子：
2.5
作者：
Dahlke, Stephan;Kutyniok, Gitta;Teschke, Gerd
通讯作者：
Teschke, Gerd