Wavelets with composite dilations
By Kanghui Guo, Demetrio Labate, Wang-Q Lim, Guido L. Weiss, E. Wilson. 2004
135 citations recorded by the source corpus.
A wavelet with composite dilations is a function generating an orthonormal basis or a Parseval frame for L2(Rn) under the action of lattice translations and dilations by products of elements drawn from non-commuting matrix sets A and B. Typically, the members of B are shear matrices (all eigenvalues are one) while the members of A are matrices expanding or contracting on a proper subspace of Rn. These wavelets are of interest in applications because of their tendency to produce “long, narrow” window functions well suited to edge detection. In this paper, we discuss the remarkable extent to which the theory of wavelets with composite dilations parallels the theory of classical wavelets, and present several examples of such systems.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/761b718d6f33fc0b06121bb047203b61a7026d1e
How researchers see this paper
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In Applied Mathematics
- Demetrio Labate
- Gitta Kutyniok
- Wang-Q Lim
- Kanghui Guo
- E.J. Candes
- David L. Donoho
- Glenn R. Easley
- Guido L. Weiss
In Computer Vision and Pattern Recognition
- Demetrio Labate
- Gitta Kutyniok
- Wang-Q Lim
- Kanghui Guo
- E.J. Candes
- Glenn R. Easley
- Laurent Demanet
- David L. Donoho
In Mechanics of Materials
- Demetrio Labate
- David L. Donoho
- E.J. Candes
- Laurent Demanet
- Gitta Kutyniok
- Felix J. Herrmann
- Gilles Hennenfent
Citations in the corpus
- Optimally Sparse Multidimensional Representation Using Shearlets (2007, background): “This is particularly useful for the development of fast algorithmic implementations of these transformations [24, 26].”
- The Theory of Wavelets with Composite Dilations (2006, background): “For example, one can construct composite wavelets with good time-frequency decay properties whose elements contain “long and narrow” waveforms with many locations, scales, shapes and directions [8].”
- Wavelets with composite dilations and their MRA properties (2006, background): “Some special examples of this construction can be found in [10] and [11, Sec.”
- Fast Discrete Curvelet Transforms (2006, background): “The idea of using concentric squares and shears is also central to the construction of tight frames of “shearlets” by Guo, Kutyniok, Labate, Lim, Weiss, and Wilson in a recent series of papers [28, 29, 30] starting with [28].”
- Sparse directional image representations using the discrete shearlet transform (2008, background): “Finally, thanks to their mathematical structure, the shearlets are associated to a multiresolution analysis (see [27,30]).”
- Resolution of the wavefront set using continuous shearlets (2006, background): “We refer to [13, 15, 16, 17, 18, 22, 21] for more detail about the research about shearlets.”