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

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