Related papers: ShearLab: A Rational Design of a Digital Parabolic…
Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. We exemplarily mention the systems of contourlets, curvelets, and…
Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. We exemplarily mention the systems of contourlets, curvelets, and…
Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation…
Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides…
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…
The shearlet transform from applied harmonic analysis is currently the state of the art when analyzing multidimensional signals with anisotropic singularities. Its optimal sparse approximation properties and its faithful digitalization…
Shearlet systems have been introduced as directional representation systems, which provide optimally sparse approximations of a certain model class of functions governed by anisotropic features while allowing faithful numerical realizations…
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…
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient…
In this paper, we propose a solution for a fundamental problem in computational harmonic analysis, namely, the construction of a multiresolution analysis with directional components. We will do so by constructing subdivision schemes which…
Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier…
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…
We introduce bendlets, a shearlet-like system that is based on anisotropic scaling, translation, shearing, and bending of a compactly supported generator. With shearing being linear and bending quadratic in spatial coordinates, bendlets…
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…
Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few…
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)…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific…
This paper is devoted to the mathematical analysis of a system of pseudo-parabolic partial differential equations governed by an energy functional, associated with anisotropic monochrome image processing. The energy functional is based on…
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…