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Authors: Persico, R. 
Title: «Paralipomena» on uniqueness in inverse scattering from a finite number of data
Issue Date: Apr-2007
Series/Report no.: 2/50 (2007)
Keywords: Fourier transform
diffraction tomography
inverse scattering
Subject Classification05. General::05.01. Computational geophysics::05.01.01. Data processing 
Abstract: 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.
Appears in Collections:Annals of Geophysics

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