Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013Harmonic analysis
|Page(s)||60 - 74|
|Published online||28 January 2013|
3D Data Denoising Using Combined Sparse Dictionaries
1 System Planning
Corporation, Arlington, VA
2 Department of Mathematics, University of Houston, Houston, Texas 77204, USA
∗ Corresponding author. E-mail: email@example.com
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.
Mathematics Subject Classification: 42C15 / 42C40
Key words: curvelets / denoising / nonlinear approximations / pursuit algorithms / shearlets / sparse approximations / wavelets
© EDP Sciences, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.