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Learning sparse representations on the sphere

Abstract : 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.
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https://hal-cea.archives-ouvertes.fr/cea-03012045
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Submitted on : Wednesday, November 18, 2020 - 1:23:55 PM
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F. Sureau, F. Voigtlaender, M. Wust, J.-L. Starck, G. Kutyniok. Learning sparse representations on the sphere. Astronomy and Astrophysics - A&A, EDP Sciences, 2019, 621, pp.A73. ⟨10.1051/0004-6361/201834041⟩. ⟨cea-03012045⟩

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