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ShearLab 3D

Gitta Kutyniok, Wang-Q Lim, Rafael Reisenhofer
2016 ACM Transactions on Mathematical Software  
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  ...  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  ...  of the transform associated with a universal compactly supported shearlet system SH(φ, ψ,ψ; α, c) (as introduced in Subsection 2.2) used in ShearLab 3D.  ... 
doi:10.1145/2740960 fatcat:t44mrn5ydbbtbgyrrplm55hh6i

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

Gitta Kutyniok, Wang-Q Lim, Rafael Reisenhofer, Technische Universität Berlin
2021
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  ...  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  ...  ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets A:5 Universal Shearlet Systems We next introduce 2D and 3D universal shearlet systems, each time first discussing  ... 
doi:10.14279/depositonce-14580 fatcat:bbvznkj5wzhffeg5nte4tlmtfu

tfShearlab: The TensorFlow Digital Shearlet Transform for Deep Learning [article]

Héctor Andrade-Loarca, Gitta Kutyniok
2020 arXiv   pre-print
With this motivation we developed a tensor shearlet transform aiming to provide a faithful TensorFlow implementation.  ...  Its optimal sparse approximation properties and its faithful digitalization allow shearlets to be applied to different problems from imaging science, such as image denoising, image inpainting, and singularities  ...  on the faithful formulation of Shearlab3D, it inherits the theoretical properties of the continuous compactly supported shearlet transform, and even gains significantly in terms of performance improvement  ... 
arXiv:2006.04591v1 fatcat:rur4ghxctvdwtljtixua4nvuxm

Discrete shearlet transform on GPU with applications in anomaly detection and denoising

Xavier Gibert, Vishal M Patel, Demetrio Labate, Rama Chellappa
2014 EURASIP Journal on Advances in Signal Processing  
In this paper, we present an open source stand-alone implementation of the 2D discrete shearlet transform using CUDA C++ as well as GPU-accelerated MATLAB implementations of the 2D and 3D shearlet transforms  ...  For example, denoising a single 512 × 512 image using a current implementation of the shearlet-based shrinkage algorithm can take between 10 s and 2 min, depending on the number of CPU cores, and much  ...  This work was supported by the Federal Railroad Administration under contract DTFR53-13-C-00032. DL acknowledges support from NSF grant DMS 1008900/1008907 and DMS 1005799.  ... 
doi:10.1186/1687-6180-2014-64 fatcat:5nmxuo4y6nacjdrwfov6bfdwnq

Shearlets as Feature Extractor for Semantic Edge Detection: The Model-Based and Data-Driven Realm [article]

Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem
2019 arXiv   pre-print
Our approach is based on a combination of the model-based concept of shearlets, which provides probably optimally sparse approximations of a model-class of images, and the data-driven method of a suitably  ...  This is based on the fact that edges in images contain most of the semantic information. Semantic edge detection involves two tasks, namely pure edge detecion and edge classification.  ...  An approach based on the shearlet transform of an image is presented in detail in Section 3.2, see also [3] .  ... 
arXiv:1911.12159v1 fatcat:hebhvk7sgjc6toglbbk2syjto4

Wavelet and shearlet-based image representations for visual servoing

Lesley-Ann Duflot, Rafael Reisenhofer, Brahim Tamadazte, Nicolas Andreff, Alexandre Krupa
2018 The international journal of robotics research  
In particular, we consider the use of multiscale image representations that are based on discrete wavelet and shearlet transforms.  ...  respectively non-subsampled discrete shearlet transforms.  ...  Acknowledgment This work is partially supported by DESWEEP project funded by the Région de Bretagne and from the project NEMRO (ANR-14-CE17-0013-001) funded by the ANR, France.  ... 
doi:10.1177/0278364918769739 fatcat:fhpscq4tyba7pln2wpwdscmede

Optimal Compressive Imaging of Fourier Data [article]

Gitta Kutyniok, Wang-Q Lim
2015 arXiv   pre-print
In this paper, we introduce a novel sampling-reconstruction scheme based on a random anisotropic sampling pattern and a compressed sensing type reconstruction strategy with a variant of dualizable shearlet  ...  Applications such as Magnetic Resonance Tomography acquire imaging data by point samples of their Fourier transform.  ...  (DS2) These systems have compactly supported elements. (DS3) Dualizable shearlet frames possess one dual frame for which a closed formula exists.  ... 
arXiv:1510.05029v1 fatcat:3atrjaxrpbarfhhpvmjqcoo7yy

Optimal Compressive Imaging of Fourier Data

Gitta Kutyniok, Wang-Q Lim
2018 SIAM Journal of Imaging Sciences  
In this paper, we introduce a novel sampling-reconstruction scheme based on a random anisotropic sampling pattern and a compressed sensing type reconstruction strategy with a variant of dualizable shearlet  ...  Applications such as Magnetic Resonance Tomography acquire imaging data by point samples of their Fourier transform.  ...  (DS2) These systems have compactly supported elements. (DS3) Dualizable shearlet frames possess one dual frame for which a closed formula exists.  ... 
doi:10.1137/16m1098541 fatcat:v5ne3q25hjhz5hgyrytc7omyte

Densely-Sampled Light Field Reconstruction [chapter]

Suren Vagharshakyan, Robert Bregovic, Atanas Gotchev
2020 Lecture Notes in Computer Science  
PROLIGHT-IAPP Marie Curie Action of the People programme of the European Unions Seventh Framework Programme, REA grant agreement 32449 and from the Academy of Finland, grant No. 137012: High-Resolution Digital  ...  We compare Haar wavelets, the compactly supported shearlets as constructed in [36] and the fast finite shearlet transform [42] .  ...  APPENDIX A CONSTRUCTION OF COMPACTLY SUPPORTED SHEARLET SYSTEM The construction of compactly supported shearlet frame elements starts with defining a 1-D multi-resolution analysis with scaling and wavelet  ... 
doi:10.1007/978-3-030-41816-8_3 fatcat:xf3snnd7gzaqxhkazfybwmchna

Asymptotic Analysis of Inpainting via Universal Shearlet Systems

Martin Genzel, Gitta Kutyniok
2014 SIAM Journal of Imaging Sciences  
One prominent example of this class are shearlets, which have the additional benefitallowing faithful implementations.  ...  One of those software packages, www.shearlab.org, even offers the flexibility of usingdifferent parameter for each scale, which is not yet covered by shearlet theory.  ...  We anticipate our results to have the following impacts: • ShearLab: A comprehensive software package for the 2D and 3D shearlet transform is available at www.shearlab.org, see also [34] .  ... 
doi:10.1137/140969452 fatcat:sar4bogwj5anzlpelxzq23e7le

Shearlet-based regularization in statistical inverse learning with an application to X-ray tomography [article]

Tatiana A. Bubba, Luca Ratti
2021 arXiv   pre-print
The p = 1 case is approached as the limit case (1,2) ∋ p → 1, by complementing numerical evidence with a (partial) theoretical analysis, based on arguments from Γ-convergence theory.  ...  study of sparsity-promoting regularization and extend the aforementioned convergence rates to work with ℓ^p-norm regularization, with p ∈ (1,2), for a special class of non-tight Banach frames, called shearlets  ...  Gitta Kutyniok, Wang-Q Lim, and Rafael Reisenhofer, Shearlab 3D: Faithful digital shearlet transforms based on compactly supported shearlets, ACM Transactions on Mathematical Software (TOMS) 42 (2016  ... 
arXiv:2112.12443v1 fatcat:5ebw43ijondsvioponakclihxe

Digital Affine Shear Transforms: Fast Realization and Applications in Image/Video Processing

Xiaosheng Zhuang
2016 SIAM Journal of Imaging Sciences  
Numerical experiments and comparisons in image/video processing show the advantages of our digital affine shear transforms over many other state-of-the-art frame-based directional transforms.  ...  Moreover, we provide the detailed algorithmic steps for both the forward and backward digital affine shear transforms.  ...  The shearlet transform at http://www.shearlab.org also has many implementations and we choose the compactly supported shearlet implementation DNST as in [22] , which has the best performance so far in  ... 
doi:10.1137/15m1048318 fatcat:z4kkbmzjazem7eg4nngcpazdg4