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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) | URI: | http://hdl.handle.net/2122/3520 | Keywords: | Fourier transform diffraction tomography inverse scattering |
Subject Classification: | 05. 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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