Learning sparse representations on the sphere
1 Laboratoire AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
2 Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany
3 Lehrstuhl für Wissenschaftliches Rechnen, Katholische Universität Eichstätt-Ingolstadt, Ostenstraße 26, 85072 Eichstätt, Germany
Accepted: 27 October 2018
Many representation systems on the sphere have been proposed in the past, such as spherical harmonics, wavelets, or curvelets. Each of these data representations is designed to extract a specific set of features, and choosing the best fixed representation system for a given scientific application is challenging. In this paper, we show that one can directly learn a representation system from given data on the sphere. We propose two new adaptive approaches: the first is a (potentially multiscale) patch-based dictionary learning approach, and the second consists in selecting a representation from among a parametrized family of representations, the α-shearlets. We investigate their relative performance to represent and denoise complex structures on different astrophysical data sets on the sphere.
Key words: methods: data analysis / methods: statistical / methods: numerical
© ESO 2019
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.