Compactly Supported Curvelet-Type Systems
We study a flexible method for constructing curvelet-type frames. These curvelet-type systems have the same sparse representation properties as curvelets for appropriate classes of smooth functions, and the flexibility of the method allows us to give a constructive description of how to construct cu...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/876315 |
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| _version_ | 1832548692065779712 |
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| author | Kenneth N. Rasmussen Morten Nielsen |
| author_facet | Kenneth N. Rasmussen Morten Nielsen |
| author_sort | Kenneth N. Rasmussen |
| collection | DOAJ |
| description | We study a flexible method for constructing curvelet-type frames. These curvelet-type systems have the same sparse representation properties as curvelets for appropriate classes of smooth functions, and the flexibility of the method allows us to give a constructive description of how to construct curvelet-type systems with a prescribed nature such as compact support in direct space. The method consists of using the machinery of almost diagonal matrices to show that a system of curvelet molecules which is sufficiently close to curvelets constitutes a frame for curvelet-type spaces. Such a system of curvelet molecules can then be constructed using finite linear combinations of shifts and dilates of a single function with sufficient smoothness and decay. |
| format | Article |
| id | doaj-art-9dcc67e5d6c34b26a6a0021233c13fa3 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-9dcc67e5d6c34b26a6a0021233c13fa32025-02-03T06:13:16ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/876315876315Compactly Supported Curvelet-Type SystemsKenneth N. Rasmussen0Morten Nielsen1Department of Mathematical Sciences, Aalborg University, Fredrik Bajersvej 7G, 9220 Aalborg East, DenmarkDepartment of Mathematical Sciences, Aalborg University, Fredrik Bajersvej 7G, 9220 Aalborg East, DenmarkWe study a flexible method for constructing curvelet-type frames. These curvelet-type systems have the same sparse representation properties as curvelets for appropriate classes of smooth functions, and the flexibility of the method allows us to give a constructive description of how to construct curvelet-type systems with a prescribed nature such as compact support in direct space. The method consists of using the machinery of almost diagonal matrices to show that a system of curvelet molecules which is sufficiently close to curvelets constitutes a frame for curvelet-type spaces. Such a system of curvelet molecules can then be constructed using finite linear combinations of shifts and dilates of a single function with sufficient smoothness and decay.http://dx.doi.org/10.1155/2012/876315 |
| spellingShingle | Kenneth N. Rasmussen Morten Nielsen Compactly Supported Curvelet-Type Systems Journal of Function Spaces and Applications |
| title | Compactly Supported Curvelet-Type Systems |
| title_full | Compactly Supported Curvelet-Type Systems |
| title_fullStr | Compactly Supported Curvelet-Type Systems |
| title_full_unstemmed | Compactly Supported Curvelet-Type Systems |
| title_short | Compactly Supported Curvelet-Type Systems |
| title_sort | compactly supported curvelet type systems |
| url | http://dx.doi.org/10.1155/2012/876315 |
| work_keys_str_mv | AT kennethnrasmussen compactlysupportedcurvelettypesystems AT mortennielsen compactlysupportedcurvelettypesystems |