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Anisotropic multiscale systems on bounded domains

: Grohs, P.; Kutyniok, G.; Ma, J.; Petersen, P.; Raslan, M.


Advances in computational mathematics 46 (2020), No.2, Art. 39, 33 pp.
ISSN: 1019-7168
ISSN: 1572-9044
Journal Article
Fraunhofer HHI ()

We establish a construction of hybrid multiscale systems on a bounded domain Ω⊂R2 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 Hs(Ω), s∈N∪{0} 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.