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| Shearlet-Zerlegung eines Auges.© Gitta Kutyniok |
A good opportunity to update a little corner of WITS: Where is the Starlet, which was beginning to grow a few webs. Mmh, look like some familiar frequency domain partitioning... And now for something completely different: number 1, the shearlet... the shearlet! (Monty Python inside)
Shearlets
| In short: | Non-separable wavelets built out of parabolic scaling, shear, and translation operations |
| Etymology: | From shear, a sheer distorsion |
| Origin: | Labate, Demetrio and Lim, W-Q. and Kutyniok, Gitta and Weiss Guido, Sparse multidimensional representation using shearlets (local copy) A handful lot of papers is available here: shearlet papers. A first overview is given in Shearlets. The First Five Year (Oberwolfach Report, 2010, local copy). |
| Some properties: | Unlike curvelets, shearlets form an affine system with a single generating mother shearlet function parameterized by a scaling, a shear, and a translation parameter. Provides the same approximation properties as curvelets, albeit with a different directional sensitivity. Exist in band-limited or compact support flavors. Possess natural, canonical smoothness spaces, called shearlet coorbit spaces, similar to Besov spaces for wavelets. Apparently extend to arbitrary any dimensions. |
| Usage: | Image denoising, restoration, morphological component analysis |
| See also: | The shearlet website, recently updated with ShearLab (... a rationally designed digital shearlet transform)
For discrete implementation, there exists for instance a Digital Shearlet Transforms or Development of a Digital Shearlet Transform Based on Pseudo-Polar FFT.
Shearlet Matlab toolboxes are available at ShearLab matlab toolboxes,
local shearlet toolbox by G. Easley and FSST:
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| Comments: | Potential a hard competitor, for years to come, to the quite oversold curvelets (IMHOlet: In My (little) Humble Opinion) |
More on the topic:
2D wavelets: A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity
