Anisotropic Multiscale Systems on Bounded Domains
METADATA ONLY
Loading...
Author / Producer
Date
2015-10
Publication Type
Report
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
In this paper we provide a construction of multiscale systems on a bounded domain \(\Omega \subset \mathbb{R}^2\) coined boundary shearlet systems, which satisfy several properties advantageous for applications to imaging science and numerical analysis of partial differential equations. More precisely, we construct boundary shearlet systems that form frames for \(L^2(\Omega)\) with controllable frame bounds and admit optimally sparse approximations for functions, which are smooth apart from a curve-like discontinuit\pp{y}. Indeed, the constructed systems allow for boundary conditions, and characterize Sobolev spaces over \(\Omega\) by their analysis coefficients. Finally, we demonstrate numerically that these systems also constitute a Gelfand frame for \((H^s(\Omega), L^2(\Omega), H^{-s}(\Omega))\) for \(s \in \mathbb{N}\).
Permanent link
Publication status
published
Editor
Book title
Journal / series
Volume
2015-30
Pages / Article No.
Publisher
Seminar for Applied Mathematics, ETH Zurich
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Organisational unit
03941 - Grohs, Philipp (ehemalig)