Optimally sparse shearlet approximations of 3D data

Abstract

Sparse representations of multidimensional data have gained more and more prominence in recent years, in response to the need to process large and multi-dimensional data sets arising from a variety of applications in a timely and effective manner. This is especially important in applications such as remote sensing, satellite imagery, scientific simulations and electronic surveillance. Directional multiscale systems such as shearlets are able to provide sparse representations thanks to their ability to approximate anisotropic features much more efficiently than traditional multiscale representations. In this paper, we show that the shearlet approach is essentially optimal in representing a large class of 3D containing discontinuities along surfaces. This is the first nonadaptive approach to achieve provably optimal sparsity properties in the 3D setting.

Department(s)

Mathematics

Document Type

Conference Proceeding

DOI

https://doi.org/10.1117/12.886227

Keywords

Affine systems, curvelets, shearlets, sparsity, wavelets

Publication Date

9-26-2011

Journal Title

Proceedings of SPIE - The International Society for Optical Engineering

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