Paper Info
Title
ShearLab 3D: Faithful Digital Shearlet Transforms Based on Compactly Supported Shearlets.
Abstract
Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient of sparsely approximating and also of 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 paper, 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 reseaerch, all scripts are accessible on www.ShearLab.org.
Year
DOI
Venue
2016
10.1145/2740960
ACM Trans. Math. Softw.
Keywords
Field
DocType
Design,Algorithms,Performance,Imaging sciences,software package,shearlets,wavelets
Mathematical optimization,CUDA,Computer science,Image processing,Algorithm,Shearlet,Feature extraction,Theoretical computer science,Inpainting,Contourlet,Wavelet,Curvelet
Journal
Volume
Issue
ISSN
42
1
0098-3500
Citations 
PageRank 
References 
20
0.78
24
Authors
3
Name
Order
Citations
PageRank
Gitta Kutyniok132534.77
Wang-Q Lim21959.41
Rafael Reisenhofer3503.09