Fast Finite Shearlet Transform (FFST)

The FFST package provides a fast implementation of the Finite Shearlet Transform. Following the the path via the continuous shearlet transform, its counterpart on cones and finally its discretization on the full grid we obtain the translation invariant discrete shearlet transform. Our discrete shearlet transform can be efficiently computed by the fast Fourier transform (FFT). The discrete shearlets constitute a Parseval frame of the finite Euclidean space such that the inversion of the shearlet transform can be simply done by applying the adjoint transform.

The FFST package provides a fast implementation of the Finite Shearlet Transform. Following the the path via the continuous shearlet transform, its counterpart on cones and finally its discretization on the full grid we obtain the translation invariant discrete shearlet transform. Our discrete shearlet transform can be efficiently computed by the fast Fourier transform (FFT). The discrete shearlets constitute a Parseval frame of the finite Euclidean space such that the inversion of the shearlet transform can be simply done by applying the adjoint transform.

Publications

• S. Häuser, G. Steidl (2014).
Fast Finite Shearlet Transform: a tutorial.
ArXiv. (1202.1773),
[pdf] [www]

• S. Häuser and G. Steidl (2013).
Convex Multiclass Segmentation with Shearlet Regularization.
International Journal of Computer Mathematics. 90, (1), 62-81.
[pdf] [doi]

Please cite both publications when using the software.

Installation

The zip-file contains all relevant files and folders. Simply unzip the archive and add the folder (with subfolders!) to your Matlab path or run installFFST.m.

The folder FFST contains the main files for the both directions of the transform. The included shearlets are stored in the folder shearlets. The folder helper contains some helper functions. To create simple geometric structures some functions are provided in create.

To check if everything is installed correctly run simple_example.m for testing.

current version (v2.0): FFST

Changelog:

• support for rectangular images
• ensure real shearlet coefficients
• compute truly complex shearlets
• usage of own shearlet spectra easier
• speed improvement
• several bugs etc. fixed

old version (v1.0): FFST v1.0