Abstract
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.
Original language | English |
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Journal | Journal of Function Spaces and Applications |
Volume | 2012 |
Issue number | Article ID 876315 |
Number of pages | 18 |
ISSN | 0972-6802 |
DOIs | |
Publication status | Published - 2012 |