####
Discrete Shearlet Transform

The shearlet transform, is a very recent sibling in the family of geometric image
representations and provides a traditional multiresolution analysis. By a specific
design of the discrete shearlet transform in [1] that we use, a lower redundancy factor
(around 2.66 or 8/3)
is possible than with most other multiresolution representations, while offering
an excellent directional analysis and even shift invariance.

Below, a visualization of different shearlet basis functions (spatial domain +
frequency domain) is given. Click on the frequency tiling on the left, to select
a particular shearlet or scaling function.

Brief explanation of the parameters:

*Scales*: the number of frequency scales for the transform.
*Max. orient*: the number of orientations for the finest scale of the
Shearlet transform (the number of orientations halves at every coarser scale).
*Angular cutoff*: determines the angular bandwidth of the shearlet
frequency responses (or consequently the size of the spatial support of the
basis functions)
*Show frequency spectrum*: if checked, the Discrete Fourier spectrum of the
basis function is shown. Otherwise, the basis function is shown in spatial
domain.

#### References

- [1] B. Goossens, J. Aelterman, H. Q. Luong, A. Pizurica and W. Philips, "Efficient Design of a Low Redundant Discrete Shearlet Transform, " in Proc. 2009 International Workshop on Local and Non-Local Approximation in Image Processing (LNLA2009), August 19-21, 2009, Tuusula, Finland (invited paper), p. 112-124