3D Data Denoising Using Combined Sparse Dictionaries

¹ System Planning Corporation, Arlington, VA 22201, USA
² Department of Mathematics, University of Houston, Houston, Texas 77204, USA

^∗ Corresponding author. E-mail: dlabate@math.uh.edu

Abstract

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.