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Learning sparse representations on the sphere
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DOI：10.1051/0004-6361/201834041.png)
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Abstract
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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 alpha-shearlets. We investigate their relative performance to represent and denoise complex structures on different astrophysical data sets on the sphere.
Keywords:
methods: data analysis
methods: statistical
methods: numerical
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