Optimally sparse shearlet approximations of 3D data

Demetrio Labate; Kanghui Guo

doi:10.1117/12.886227

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3 June 2011 Optimally sparse shearlet approximations of 3D data

Demetrio Labate, Kanghui Guo

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Proceedings Volume 8058, Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering IX; 805807 (2011) https://doi.org/10.1117/12.886227
Event: SPIE Defense, Security, and Sensing, 2011, Orlando, Florida, United States

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.

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Demetrio Labate and Kanghui Guo "Optimally sparse shearlet approximations of 3D data", Proc. SPIE 8058, Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering IX, 805807 (3 June 2011); https://doi.org/10.1117/12.886227

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