«Paralipomena» on uniqueness in inverse scattering from a finite number of data
Main Article Content
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.
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.
Article Details
How to Cite
Persico, R. (2007) “«Paralipomena» on uniqueness in inverse scattering from a finite number of data”, Annals of Geophysics, 50(2). doi: 10.4401/ag-3076.
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