Journal
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
Volume 8, Issue 1, Pages 60-74Publisher
EDP SCIENCES S A
DOI: 10.1051/mmnp/20138104
Keywords
curvelets; denoising; nonlinear approximations; pursuit algorithms; shearlets; sparse approximations; wavelets
Categories
Funding
- NSF [DMS 1008900, DMS 1005799]
- NHARP [003652-0136-2009]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1005799] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1008900] Funding Source: National Science Foundation
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Directional multiscale representations such as shearlets and curvelets have gained increasing recognition in recent years as superior methods for the sparse representation of data. Thanks to their ability to sparsely encode images and other multidimensional data, transform-domain denoising algorithms based on these representations are among the best performing methods currently available. As already observed in the literature, the performance of many sparsity-based data processing methods can be further improved by using appropriate combinations of dictionaries. In this paper, we consider the problem of 3D data denoising and introduce a denoising algorithm which uses combined sparse dictionaries. Our numerical demonstrations show that the realization of the algorithm which combines 3D shearlets and local Fourier bases provides highly competitive results as compared to other 3D sparsity-based denosing algorithms based on both single and combined dictionaries.
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