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We introduce one- and two-dimensional `exponential shapelets': orthonormalbasis functions that efficiently model isolated features in data. They arebuilt from eigenfunctions of the quantum mechanical hydrogen atom, and inheritmathematics with elegant properties under Fourier transform, and hence(de)convolution. For a wide variety of data, exponential shapelets compressinformation better than Gauss-Hermite/Gauss-Laguerre (`shapelet')decomposition, and generalise previous attempts that were limited to 1D orcircularly symmetric basis functions. We discuss example applications inastronomy, fundamental physics and space geodesy.

Exponential shapelets: basis functions for data analysis of isolated features