Fast Finite Shearlet Transform
For researchers needing efficient directional analysis, this offers a practical FFT-based implementation, though it is a tutorial rather than a novel algorithmic breakthrough.
This tutorial presents a fast finite shearlet transform based solely on the FFT, constructing a Parseval frame for a simple inverse transform. It provides proofs and implementation details for directional information retrieval.
In recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the continuous shearlet transform has the outstanding property to stem from a square integrable group representation. However, to use shearlets and the shearlet transform for reasonable applications one needs fast algorithms to compute a discrete shearlet transform. In this tutorial we present the steps towards an implementation of a fast and finite shearlet transform that is only based on the FFT. Using band-limited shearlets we construct a Parseval frame that provides a simple and straightforward inverse shearlet transform. We provide all proofs and discuss several aspects of our implementation.