Name
Abstract | ||
|---|---|---|
In this paper, we first introduce the concept of an adaptive multiresolution analysis (AMRA) structure, which is a variant of the classical MRA structure well suited to the main goal of a fast flexible decomposition strategy adapted to the data at each decomposition level. We then study this novel methodology for the general case of affine-like systems and derive a unitary extension principle (UEP) for filter design. Finally, we apply our results to the directional representation system of shearlets. This leads to a comprehensive theory for fast decomposition algorithms associated with shearlet systems which encompasses tight shearlet frames with spatially compactly supported generators within such an AMRA structure. Also, shearlet-like systems associated with parabolic scaling and unimodular shear matrices are studied within this framework. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/090780912 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
shearlet system,decomposition level,adaptive multiresolution analysis structures,classical mra structure,shearlet systems,affine-like system,adaptive multiresolution analysis,fast flexible decomposition strategy,comprehensive theory,amra structure,tight shearlet frame,fast decomposition,shearlets | Mathematical optimization,Mathematical analysis,Matrix (mathematics),Multiresolution analysis,Shearlet,Unitary state,Unimodular matrix,Scaling,Mathematics,Filter design,Parabola | Journal |
Volume | Issue | ISSN |
49 | 5 | 0036-1429 |
Citations | PageRank | References |
11 | 0.81 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bin Han | 1 | 93 | 13.23 |
| Gitta Kutyniok | 2 | 325 | 34.77 |
| Zuowei Shen | 3 | 3131 | 155.87 |