ShearLab 3D

Author(s)
G. Kutyniok, W.-Q. Lim, R. Reisenhofer
Abstract

Wavelets and their associated transforms are highly efficient when approximating and analyzing onedimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient in sparsely approximating and also in analyzing in the sense of, for instance, detecting their direction. Shearlets are a directional representation system extending the wavelet framework, which overcomes those deficiencies. Similar to wavelets, shearlets allow a faithful implementation and fast associated transforms. In this article, we will introduce a comprehensive carefully documented software package coined ShearLab 3D (www.ShearLab.org) and discuss its algorithmic details. This package provides MATLAB code for a novel faithful algorithmic realization of the 2D and 3D shearlet transform (and their inverses) associated with compactly supported universal shearlet systems incorporating the option of using CUDA. We will present extensive numerical experiments in 2D and 3D concerning denoising, inpainting, and feature extraction, comparing the performance of ShearLab 3D with similar transform-based algorithms such as curvelets, contourlets, or surfacelets. In the spirit of reproducible research, all scripts are accessible on www.ShearLab.org.

Organisation(s)
External organisation(s)
Universität Bremen, Technische Universität Berlin
Journal
ACM Transactions on Mathematical Software
Volume
42
Pages
1-42
No. of pages
42
ISSN
0098-3500
DOI
https://doi.org/10.1145/2740960
Publication date
01-2016
Peer reviewed
Yes
Austrian Fields of Science 2012
101032 Functional analysis, 101014 Numerical mathematics
Keywords
ASJC Scopus subject areas
Software, Applied Mathematics
Portal url
https://ucrisportal.univie.ac.at/en/publications/fb569e29-a971-406d-a70d-5da8fcc2fce2