Anisotropic multiscale systems on bounded domains

Grohs, Philipp; Kutyniok, Gitta ; Ma, Jackie; Petersen, Philipp und Raslan, Mones (2020): Anisotropic multiscale systems on bounded domains. In: Advances in Computational Mathematics, Vol. 46, 39

Abstract

We establish a construction of hybrid multiscale systems on a bounded domain consisting of shearlets and boundary-adapted wavelets, which satisfy several properties advantageous for applications to imaging science and the numerical analysis of partial differential equations. More precisely, we construct hybrid shearlet-wavelet systems that form frames for the Sobolev spaces with controllable frame bounds and admit optimally sparse approximations for functions which are smooth apart from a curve-like discontinuity. Per construction, these systems allow to incorporate boundary conditions.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1019-7168
• Language: English