Exponential shapelets: basis functions for data analysis of isolated features

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