Cone-adapted bandlimited shearlet system

The `shearletSystem`

object represents a cone-adapted
bandlimited shearlet system. After you create the shearlet system, you can use `sheart2`

to
obtain the shearlet transform of a real-valued 2-D image. You can also use `isheart2`

to
obtain the inverse transform. Additional Object Functions are
provided.

creates a cone-adapted
real-valued bandlimited shearlet system for a real-valued image of size 128-by-128 with
the number of scales equal to 4. The system `sls`

= shearletSystem`sls`

is a nondecimated
shearlet system. Shearlets extending beyond the 2-D frequency bounds are periodically
extended. Using real-valued shearlets with periodic boundary conditions results in
real-valued shearlet coefficients.

The implementation of `shearletSystem`

follows the approach described in Häuser and Steidl [6]

creates a cone-adapted bandlimited shearlet system with Properties specified by one or
more `sls`

= shearletSystem(`Name,Value`

)`Name,Value`

pairs. For example,
`shearletSystem('ImageSize',[100 100])`

creates a shearlet system for
images of size 100-by-100. Properties can be specified in any order as
`Name1,Value1,...,NameN,ValueN`

. Enclose each property name in single
quotes (`' '`

) or double quotes (`" "`

).

Property values of a shearlet system are fixed. For example, if the shearlet
system `SLS`

is created with an `ImageSize`

of [128
128], you cannot change that `ImageSize`

to [200 200].

`sheart2` | Shearlet transform |

`isheart2` | Inverse shearlet transform |

`framebounds` | Shearlet system frame bounds |

`filterbank` | Shearlet system filters |

`numshears` | Number of shearlets |

[1] Guo, K., G. Kutyniok, and D.
Labate. "Sparse multidimensional representations using anisotropic dilation and shear
operators." In *Wavelets and Splines: Athens 2005* (G. Chen, and M.-J.
Chen, eds.), 189–201. Brentwood, TN: Nashboro Press, 2006.

[2] Guo, K., and D. Labate. "Optimally
Sparse Multidimensional Representation Using Shearlets." *SIAM Journal on
Mathematical Analysis*. Vol. 39, Number 1, 2007, pp. 298–318.

[3] Kutyniok, G., and W.-Q Lim.
"Compactly supported shearlets are optimally sparse." *Journal of Approximation
Theory*. Vol. 163, Number 11, 2011, pp. 1564–1589.

[4] *Shearlets: Multiscale
Analysis for Multivariate Data* (G. Kutyniok, and D. Labate, eds.). New York:
Springer, 2012.

[5] *ShearLab*.
`https://www3.math.tu-berlin.de/numerik/www.shearlab.org/`

.

[6] Häuser, S., and G. Steidl. "Fast Finite Shearlet Transform: a tutorial." arXiv preprint arXiv:1202.1773 (2014).