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Preprint 21-2014

ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets

Source file is available as :   Portable Document Format (PDF)

Author(s) : Gitta Kutyniok , Wang-Q Lim , Rafael Reisenhofer

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 21-2014

MSC 2000

94A08 Image processing
65T60 Wavelets

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 incorporat- ing 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.

Keywords : Design, Algorithms, Performance, Imaging Sciences, Software Package, Shearlets, Wavelet

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