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Related papers: Compactly Supported Shearlets

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It is known that the continuous wavelet transform of a function $f$ decays very rapidly near the points where $f$ is smooth, while it decays slowly near the irregular points. This property allows one to precisely identify the singular…

Functional Analysis · Mathematics 2007-05-23 Gitta Kutyniok , Demetrio Labate

Image classifiers are known to be difficult to interpret and therefore require explanation methods to understand their decisions. We present ShearletX, a novel mask explanation method for image classifiers based on the shearlet transform --…

Computer Vision and Pattern Recognition · Computer Science 2023-05-01 Stefan Kolek , Robert Windesheim , Hector Andrade Loarca , Gitta Kutyniok , Ron Levie

Anisotropic decompositions using representation systems such as curvelets, contourlet, or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse approximations of…

Functional Analysis · Mathematics 2015-03-17 Gitta Kutyniok

In this paper, we present an image separation method for separating images into point- and curvelike parts by employing a combined dictionary consisting of wavelets and compactly supported shearlets utilizing the fact that they sparsely…

Numerical Analysis · Mathematics 2011-06-13 Gitta Kutyniok , Wang-Q Lim

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…

Numerical Analysis · Mathematics 2014-07-24 S. Häuser , G. Steidl

The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…

Information Theory · Computer Science 2017-02-16 Renato Budinich

Segmentation plays an important role in many preprocessing stages in image processing. Recently, convex relaxation methods for image multi-labeling were proposed in the literature. Often these models involve the total variation (TV)…

Numerical Analysis · Mathematics 2012-05-17 S. Häuser , G. Steidl

The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by…

Functional Analysis · Mathematics 2016-01-11 Axel Flinth , Martin Schäfer

We develop an algorithm for single-image superresolution of remotely sensed data, based on the discrete shearlet transform. The shearlet transform extracts directional features of signals, and is known to provide near-optimally sparse…

Computer Vision and Pattern Recognition · Computer Science 2018-09-05 Wojciech Czaja , James M. Murphy , Daniel Weinberg

Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse…

Functional Analysis · Mathematics 2012-06-12 Philipp Grohs , Gitta Kutyniok

The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based…

Numerical Analysis · Mathematics 2019-07-04 Amir Averbuch , Pekka Neittaanmaki , Valery Zheludev

Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…

Computer Vision and Pattern Recognition · Computer Science 2019-11-12 Xiaohao Cai , Christopher G. R. Wallis , Jennifer Y. H. Chan , Jason D. McEwen

In this paper, we introduce Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine elements from Gabor and wavelet frames in their construction.…

Functional Analysis · Mathematics 2013-03-27 Bernhard G. Bodmann , Gitta Kutyniok , Xiaosheng Zhuang

We consider the problem of characterizing the Sobolev wavefront set of a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous wavelet transform, with the latter being defined with respect to a suitably chosen…

Functional Analysis · Mathematics 2024-02-06 Hartmut Führ , Mahya Ghandehari

Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…

Numerical Analysis · Computer Science 2018-05-08 Christian Lessig

A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…

Numerical Analysis · Mathematics 2025-04-29 Yanchuang Cao , Jun Liu , Dawei Chen

Recently, compressed sensing techniques in combination with both wavelet and directional representation systems have been very effectively applied to the problem of image inpainting. However, a mathematical analysis of these techniques…

Functional Analysis · Mathematics 2012-11-29 Emily J. King , Gitta Kutyniok , Xiaosheng Zhuang

This paper presents a new approach for 3D shape generation, inversion, and manipulation, through a direct generative modeling on a continuous implicit representation in wavelet domain. Specifically, we propose a compact wavelet…

Computer Vision and Pattern Recognition · Computer Science 2023-02-02 Jingyu Hu , Ka-Hei Hui , Zhengzhe Liu , Ruihui Li , Chi-Wing Fu

This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly…

Analysis of PDEs · Mathematics 2007-05-23 Emmanuel J. Candes , Laurent Demanet

With the increasing growth of technology and the entrance into the digital age, we have to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an…

Multimedia · Computer Science 2012-08-15 Kamrul Hasan Talukder , Koichi Harada