Please use this identifier to cite or link to this item:
http://hdl.handle.net/2122/3520| DC Field | Value | Language |
|---|---|---|
| dc.contributor.authorall | Persico, R.; Istituto per i Beni Archeologici e Monumentali (IBAM), CNR, Lecce, Italy | en |
| dc.date.accessioned | 2007-12-31T09:32:01Z | en |
| dc.date.available | 2007-12-31T09:32:01Z | en |
| dc.date.issued | 2007-04 | en |
| dc.identifier.uri | http://hdl.handle.net/2122/3520 | en |
| dc.description.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. | en |
| dc.language.iso | English | en |
| dc.relation.ispartofseries | 2/50 (2007) | en |
| dc.subject | Fourier transform | en |
| dc.subject | diffraction tomography | en |
| dc.subject | inverse scattering | en |
| dc.title | «Paralipomena» on uniqueness in inverse scattering from a finite number of data | en |
| dc.type | article | en |
| dc.type.QualityControl | Peer-reviewed | en |
| dc.subject.INGV | 05. General::05.01. Computational geophysics::05.01.01. Data processing | en |
| dc.relation.references | ALBERTI, G., L. CIOFANIELLO, M. DELLA NOCE, S. ESPOSITO, G. GALIERO, R. PERSICO, M. SACCHETTINO and S. VETRELLA (2002): A stepped frequency GPR system for underground prospecting, Ann. Geophysics, 45 (2), 375- 391. ALBERTI, G., L. CIOFANIELLO, G. GALIERO, R. PERSICO, M. SACCHETTINO, G.M. SIGNORE and S. VETRELLA (2003): Experimental results from a stepped frequency GPR, Ann. Geophysics, 46 (4), 707-717. BERTERO, M. and P. BOCCACCI (1998): Introduction to Inverse Problems in Imaging (Taylor & Francis), pp. 352. CATAPANO, I., L. CROCCO, R. PERSICO, M. PIERACCINI and F. SOLDOVIERI (2006): Linear and non-linear microwave tomography approaches for subsurface prospecting: validation on real data, IEEE Trans. Antennas Wireless Propag. Lett., 5, 49-53. CHEW, W.C. (1995): Waves and Fields in Inhomogeneous Media (IEEE Press, Piscataway, N.J.), pp. 608. CLEMMOW, P.C. (1996): The Plane Wave Spectrum Representation of Electromagnetic Field (Wiley-IEEE Press), pp. 198. COLTON, D. and L. PAIVARINTA (1992): The uniqueness of a solution to an inverse scattering problem for electromagnetic waves, Arch. Rational Mech. Anal., 119, 59-70. CROCCO, L. and F. SOLDOVIERI (2003): GPR prospecting in a layered medium via microwave tomography, Ann. Geophysics, 46, 559-572. DANIELS, D. (2004): Ground Penetrating Radar (Inspec/Iee), 2nd edition, pp. 734. DEVANEY, A.J. (1978): Nonuniqueness in the inverse scattering problem, J. Math. Phys., 19, 1526-1531. FISHER, M. and K.J. LANGENBERG (1984): Limitations and defects of certain inverse scattering theories, IEEE Trans. Antennas Propag., AP-32, 1080-1088. HANSEN, T.B. and P.M. JOHANSEN (2000): Inversion scheme for ground penetrating radar that takes into account the planar air-soil interface, IEEE Trans. Geosci. Remote Sensing, 38, 496-506. KANTOROVIC, L.V. and G.P. AKILOV (1982): Functional Analysis (Pergamon Press), 2nd edition, pp. 589. LEONE, G. and F. SOLDOVIERI (2003): Analysis of the distorted Born approximation for subsurface reconstruction: truncation and uncertainties effects, IEEE Trans. Geosci. Remote Sensing, 41, 66-74. LESSELIER, D. and B. DUCHENE (1996):Wavefield inversion of objects in stratified environments: from back-propagation schemes to full solutions, in Review of Radio Science 1993-1996, edited by R. STONE (Oxford University Press, Oxford), 235-268. LEVIN, B. (1980): Distribution of Zeros of Entire Functions (Providence, R.I., Am. Math. Soc.), 2nd edition, pp. 523. LEVINSON, N. (1940): Gap and Density Theorems (Am. Math. Soc.), pp. 246. MEINCKE, P. (2001): Linear GPR inversion for lossy soil and a planar air-soil interface, IEEE Trans. Geosci. Remote Sensing, 39, 2713-2721. PALEY, R. and N. WIENER (1934): Fourier Transform in the Complex Domain (Am. Math. Soc., New York)). PERSICO, R. and F. SOLDOVIERI (2004a): Reconstruction of a slab embedded in a three layered medium from multifrequency data under Born approximation, J. Optical Soc. Am. A, 21, 35-45. PERSICO, R. and F. SOLDOVIERI (2004b): Effects of uncertainty on background permittivity in one dimensional linear inverse scattering, J. Optical Soc. Am. A, 21, 2334-2343. PERSICO, R., R. BERNINI and F. SOLDOVIERI (2005): On the configuration of the measurements in inverse scattering from buried objects under the distorted Born approximation, IEEE Trans. Antennas Propag., 53, 1875-1886. PERSICO, R., F. SOLDOVIERI and G. LEONE (2006): A microwave tomographic approach for multibistatic configuration: the choice of the frequency step, IEEE Trans. Instrum. Meas., 55 (6), 1926-1934, doi: 10.1109/ TIM.2006.884346. PIERRI, R., R. PERSICO and R. BERNINI (1999): Information content of Born field scattered by an embedded slab: multifrequency, multiview, and multivifrequency-multiview cases, J. Optical Soc. Am. A, 16, 2392-2399. RAMM, A.G. (1990): Completeness of the products of solutions of PDE and inverse problems, Inverse Problems, 6, 643-664. SHEEN, D. and D. SHEPELSKY (2000): Uniqueness in a frequency- domain inverse problem of a stratified uniaxial bianisotropic medium, Wave Motion, 31, 371-385. SLEPIAN, D. and H.O. POLLACK (1961): Prolate spheroidal wavefunctions, Fourier analysis and uncertainty I, Bell Syst. Tech. J., 40, 43-64. SOLDOVIERI, F. and R. PERSICO (2004): Reconstruction of an embedded slab with Born approximation from multifrequency data, IEEE Trans. Antennas Propag., 52, 2348-2356. SOLDOVIERI, F., R. PERSICO and G. LEONE (2005a): Effect of source and receiver radiation characteristics in subsurface prospecting within the DBA, Radio Science, 40, RS3006. SOLDOVIERI, F., R. PERSICO and G. LEONE (2005b): Frequency diversity in a linear inversion algorithm for GPR prospecting, Subsurface Sensing Technol. Appl., 6, 25-42. | en |
| dc.description.journalType | JCR Journal | en |
| dc.description.fulltext | open | en |
| dc.contributor.author | Persico, R. | en |
| dc.contributor.department | Istituto per i Beni Archeologici e Monumentali (IBAM), CNR, Lecce, Italy | en |
| item.openairetype | article | - |
| item.cerifentitytype | Publications | - |
| item.languageiso639-1 | en | - |
| item.grantfulltext | open | - |
| item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
| item.fulltext | With Fulltext | - |
| crisitem.author.dept | Istituto per i Beni Archeologici e Monumentali (IBAM-CNR), Lecce, Italy | - |
| crisitem.classification.parent | 05. General | - |
| Appears in Collections: | Annals of Geophysics | |
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| 03Persico.pdf | 592.89 kB | Adobe PDF | View/Open |
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