Exponential shapelets: basis functions for data analysis of isolated features

Bergé, J.; Massey, R.; Baghi, Q.; Touboul, P.

Abstract

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 generalize previous attempts that were limited to 1D or circularly symmetric basis functions. We discuss example applications in astronomy, fundamental physics, and space geodesy.

Citation

Bergé, J., Massey, R., Baghi, Q., & Touboul, P. (2019). Exponential shapelets: basis functions for data analysis of isolated features. Monthly Notices of the Royal Astronomical Society, 486(1), 544-559. https://doi.org/10.1093/mnras/stz787

• Journal Article Type: Article
• Acceptance Date: Mar 8, 2019
• Online Publication Date: Mar 16, 2019
• Publication Date: Jun 30, 2019
• Deposit Date: Jun 25, 2019
• Publicly Available Date: Jul 2, 2019
• Journal: Monthly Notices of the Royal Astronomical Society
• Print ISSN: 0035-8711
• Electronic ISSN: 1365-2966
• Publisher: Royal Astronomical Society
• Peer Reviewed: Peer Reviewed
• Volume: 486
• Issue: 1
• Pages: 544-559
• DOI: https://doi.org/10.1093/mnras/stz787
• Public URL: https://durham-repository.worktribe.com/output/1328128