Exponential shapelets: basis functions for data analysis of isolated features. (arXiv:1903.05837v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Berge_J/0/1/0/all/0/1">Joel Bergé</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Massey_R/0/1/0/all/0/1">Richard Massey</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Baghi_Q/0/1/0/all/0/1">Quentin Baghi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Touboul_P/0/1/0/all/0/1">Pierre Touboul</a>
We introduce one- and two-dimensional `exponential shapelets’: orthonormal
basis functions that efficiently model isolated features in data. They are
built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit
mathematics with elegant properties under Fourier transform, and hence
(de)convolution. For a wide variety of data, exponential shapelets compress
information better than Gauss-Hermite/Gauss-Laguerre (`shapelet’)
decomposition, and generalise previous attempts that were limited to 1D or
circularly symmetric basis functions. We discuss example applications in
astronomy, fundamental physics and space geodesy.
We introduce one- and two-dimensional `exponential shapelets’: orthonormal
basis functions that efficiently model isolated features in data. They are
built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit
mathematics with elegant properties under Fourier transform, and hence
(de)convolution. For a wide variety of data, exponential shapelets compress
information better than Gauss-Hermite/Gauss-Laguerre (`shapelet’)
decomposition, and generalise previous attempts that were limited to 1D or
circularly symmetric basis functions. We discuss example applications in
astronomy, fundamental physics and space geodesy.
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