We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modeling 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.
Feature augmentation for the inversion of the Fourier transform with limited data / Perracchione, E.; Massone, A. M.; Piana, M.. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - ELETTRONICO. - 37:10(2021), p. 105001. [10.1088/1361-6420/ac1ad7]
Titolo: | Feature augmentation for the inversion of the Fourier transform with limited data | |
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Data di pubblicazione: | 2021 | |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1088/1361-6420/ac1ad7 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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Perracchione_2021_Inverse_Problems_37_105001.pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia | |
FeatureIP_archive.pdf | 2. Post-print / Author's Accepted Manuscript | ![]() | Embargo: 27/08/2022 Richiedi una copia |
http://hdl.handle.net/11583/2956964