Feature augmentation for the inversion of the Fourier transform with limited data. (27th August 2021)

• Record Type: Journal Article
• Authors: Perracchione, Emma; Massone, Anna Maria; Piana, Michele
• Is Part Of: Inverse problems. Volume 37:Number 10(2021)
• Publication Date: 2021-08-27
• Subjects: shape-driven interpolation -- variably scaled kernels (VSKs) -- feature augmentation -- solar x-ray imaging; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac1ad7
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.