Name
Title | ||
|---|---|---|
Optimally Sparse Approximations of 3D Functions by Compactly Supported Shearlet Frames. |
Abstract | ||
|---|---|---|
We study efficient and reliable methods of capturing and sparsely representing anisotropic structures in 3D data. As a model class for multidimensional data with anisotropic features, we introduce generalized 3D cartoon-like images. This function class will have two smoothness parameters: one parameter beta controlling classical smoothness and one parameter alpha controlling anisotropic smoothness. The class then consists of piecewise C-beta-smooth functions with discontinuities on a piecewise C-alpha-smooth surface. We introduce a pyramid-adapted, hybrid shearlet system for the 3D setting and construct frames for L-2(R-3) with this particular shearlet structure. For the smoothness range 1 < alpha <= beta <= 2 we show that pyramid-adapted shearlet systems provide a nearly optimally sparse approximation rate within the generalized cartoon-like image model class measured by means of nonlinear N-term approximations. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1137/110844726 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
anisotropic features,multidimensional data,shearlets,cartoon-like images,nonlinear approximations,sparse approximations | Anisotropy,Classification of discontinuities,Mathematical analysis,Sparse approximation,Approximations of π,Shearlet,Smoothness,Piecewise,Mathematics | Journal |
Volume | Issue | ISSN |
44 | 4 | 0036-1410 |
Citations | PageRank | References |
9 | 0.56 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gitta Kutyniok | 1 | 325 | 34.77 |
| Jakob Lemvig | 2 | 24 | 3.89 |
| Wang-Q Lim | 3 | 195 | 9.41 |