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arXiv · 2102.03755

Feature augmentation for the inversion of the Fourier transform with limited data

Emma Perracchione·Anna Maria Massone·Michele Piana
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Abstract

We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven interpolation based on Variably Scaled Kernels (VSKs), whose implementation is here tailored for inverse problems. The so-constructed interpolants are used as inputs for a standard iterative inversion scheme. After providing theoretical results concerning the spectrum of the VSK collocation matrix, we test the method on astrophysical imaging benchmarks.

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Emma Perracchione, Anna Maria Massone, Michele Piana. 2021-02-07. Feature augmentation for the inversion of the Fourier transform with limited data. https://doi.org/10.1088/1361-6420%2Fac1ad7

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