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3D Data Denoising Using Combined SparseDictionaries

Published online by Cambridge University Press:  28 January 2013

G. Easley ,
D. Labate  and
P. Negi
G. Easley
Affiliation:
System Planning Corporation, Arlington, VA 22201, USA
D. Labate*
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204, USA
P. Negi
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204, USA
*
∗ Corresponding author. E-mail: dlabate@math.uh.edu
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Abstract

Directional multiscale representations such as shearlets and curvelets have gainedincreasing recognition in recent years as superior methods for the sparse representationof data. Thanks to their ability to sparsely encode images and other multidimensionaldata, transform-domain denoising algorithms based on these representations are among thebest performing methods currently available. As already observed in the literature, theperformance of many sparsity-based data processing methods can be further improved byusing appropriate combinations of dictionaries. In this paper, we consider the problem of3D data denoising and introduce a denoising algorithm which uses combined sparsedictionaries. Our numerical demonstrations show that the realization of the algorithmwhich combines 3D shearlets and local Fourier bases provides highly competitive results ascompared to other 3D sparsity-based denosing algorithms based on both single and combineddictionaries.

Keywords

curveletsdenoisingnonlinear approximationspursuit algorithmsshearletssparse approximationswavelets
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 1: Harmonic analysis , 2013 , pp. 60 - 74
Copyright
© EDP Sciences, 2013

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