«Paralipomena» on uniqueness in inverse scattering from a finite number of data

R. Persico


This paper shows new proof of non-uniqueness of the solution for the retrieving of a compact-supported function
starting from a finite number of samples of its spectrum. As will be shown, this is relevant for linear inverse
scattering problems, that in many cases can be recast as the reconstruction of a compact supported function from
a finite set of samples of its spectrum. Since this reconstruction is not unique, from a practical point of view, any
linear inverse scattering algorithm that can be recast in terms of a Fourier relationship between unknowns and
data necessarily «trusts» on the absence of invisible objects in the particular situation at hand.


Fourier transform;diffraction tomography;inverse scattering

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DOI: https://doi.org/10.4401/ag-3076
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Published by INGV, Istituto Nazionale di Geofisica e Vulcanologia - ISSN: 2037-416X