Inverse Problems/Tomography

Selection of Interesting Papers in relationship to inverse problems in the framework of the GPR prospecting

Raffaele Persico

July 10, 2012


1. D. Slepian and H. O. Pollack, "Prolate spheroidal wavefunctions, Fourier analysis and uncertainty. I", Bell Syst. Tech. J. 40, 43-64 (1961).

2. J. H. Richmond, ‘‘Scattering by a dielectric cylinder of arbitrary cross section shape,’’ IEEE Trans. Antennas Propag. 13,334–341 (1965).

3. W. A. Schneider, Integral formulation for migration in two and three dimensions, Geophysics, vol. 43, n. 1, pp. 49-76, 1978

4. R. H. Stolt, “Migration by Fourier Transform”, Geophysics, vol. 43, n. 1, pp. 23-48, 1978.

5. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrasonic Imaging, vol. 4, pp. 336–350, 1982.

6. M. Slaney, A.C. Kak, L.E. Larsen, “Limitations of imaging with first order diffraction tomography”, IEEE Trans. Microwave Theory Techn., vol MTT-32, pp 860-874, 1984.

7. L. Chommeloux, C. Pichot, J. C. Bolomey, “Electromagnetic modeling for microwave imaging of cylindrical buried inhomogeneities”, IEEE Trans. Microwave Theory and Techniques, vol. MTT-34, n. 10, pp. 1064-1076, Oct. 1986.

8. W. Tabbra, B. Duchene, Ch. Pichot, D. Lesselier, L. Chommeloux and N. Joachimowicz, “Diffraction Tomography: Contribution to the analysis of some applications in microwave and ultrasonics, Inverse problems, vol. 4, pp. 305-331, 1988.

9. M.Idemen and I. Ackduman, “Two dimensional inverse scattering problerms connected with bodies buried in a slab”, Inverse Problems, vol. 6, pp. 749-766, 1990.

10. M. Moghaddam and W. C. Chew, nonlinear two-dimensional Velocity profile Inversion Using time Domain Data, IEEE Trans. on Geos. And remote sensing, vol. 30, n. 1, pp. 147-156, 1992.

11. J.E. Molyneux, A. Witten, “Diffraction tomographic imaging in a monostatic measurement configuration”, IEEE Trans. on Geoscience and Remote Sensing, vol. 31, no.2, pp. 507-511, 1993.

12. A. J. Witten, J. E. Molyneux and J. E. Nyquist, “Ground Penetrating Radar Tomography: Algorithms and Case Studies, “ IEEE Trans. Geoscience and Remote Sensing, vol. 32, n. 2, pp. 461-467, Mar. 1994.

13. G. P. Otto and W. C. Chew, “Microwave inverse scattering-local shape function imaging for improved resolution of strong scatterers”, IEEE Trans. on Microwave theory and techniques, vol. 42, n. 3, January 1994.

14. D. Lesselier, B. Duchene, “Wavefield inversion of objects in stratified environments: from back-propagation schemes to full solutions”, in Review of Radio Science 1993-1996, ed. R. Stone, Oxford University press, 1996.

15. R. Deming, A. J. Devaney, A Filtered Backpropagation Algorithm for GPR, Journal of Environmental & Engineering Geophysics, vol. 0, n. 2, January 1996.

16. A. Franchois, C. Pichot, Microwave imaging-complex permittivity reconstruction with a Levenberg-Marquardt method, IEEE trans. On antennas and propagation, vol. 45, n. 2, pp. 203-215, 1997.

17. D. Pommet, R. A. Marr, U. H. W. Lammers, R. V. McGahan, J. B. Morris and M. A. Fiddy, “Imaging using limited-angle backscattered data”, IEEE Trans. On Antennas and Propagation Magazine, vol. 39, n. 2, pp. 19-22, April 1997.

18. R. W. Deming and A. J. Devaney, “Diffraction tomography for multi-monostatic ground penetrating radar imaging, Inverse Problems, vol. 13, pp. 29-45, 1997.

19. B. Chen and J. J Stamnes, "Validity of diffraction tomography based on the first Born and first Rytov approximations", Appl. Opt. 37, 2996-3006, 1998.

20. T. B. Hansen and M. Johansen, “Inversion Scheme for Ground Penetrating Radar That Takes into Account the Planar Air-Soil Interface”, IEEE Trans. on Geos. and Rem. Sens., vol. 38, n. 1, pp. 496-506, January 2000.

21. C. Dourthe, C. Pichot, J. Y. Dauvignac, J. Cariou, “Inversion algorithm and measurement system for microwave tomography of buried object”, Radio Science, vol. 35 , no. 5 , pp. 1097-1108, 2000.

22. P. Meincke, “Linear GPR inversion for lossy soil and a planar air-soil interface”, IEEE Trans. on Geoscience and Remote Sensing, vol. 39, no.12, pp. 2713-2721, Dec. 2001.

23. A.G. Tijhuis, A.C. Belkebir, A.C.S. Litman, B.P. de Hon, “Theoretical and computational aspects of two dimensional inverse profiling”, IEEE Trans. Geoscience and Remote Sensing., vol. 39, n. 6, pp. 1316-1330, Jun. 2001.

24. T.J. Cui, W.C. Chew, “Diffraction tomographic algorithm for the detection of three-dimensional objects buried in a lossy half-space”, IEEE Trans. on Antennas and Propagation, vol. 50, no.1, pp. 42-49, Jan. 2002

25. P. M Meincke and T. B. Hansen, Plane wave characterization of antennas close to a plane interface, IEEE Trans. on Geoscience and Remote Sensing, vol. 42, n. 6, pp. 1222-1232, 2004.

26. A. Abubakar, P. M. van den Berg, S. Y. Semenov, “A Robust Iterative Method for Born Inversion”, IEEE Transaction on Geoscience and Remote Sensing, vol. 42, no. 2, pp. 342-354, 2004.

27. T. J. Cui, W. C. Chew, X. X. Yin, W. Hong, “Study of Resolution and Super Resolution in Electromagnetic Imaging for Half space problems”, IEEE Transaction on Antennas and Propagation, vol. 52, n. 6, pp. 1398-1411, 2004.

28. R. Persico, R. Bernini, F. Soldovieri, “On the configuration of the measurements in inverse scattering from buried objects under the distorted Born approximation”, IEEE Trans. on Antennas and Prop., vol. 53, n. 6, pp. 1875-1886, June 2005.

29. E. Slob, D. Draganov, K. Wapenaar, Interferometric Electromagnetic Green’s functions representations using propagation invariants, Geophysical Journal International, vol. 169, pp. 60-80, 2007.

30. C. P. Oden, M. H. Powers, D. L. Wright, G. R. Olhoeft, Improving GPR Image resolution in Lossy ground Using Dispersive Migration, IEEE Trans. on Geos. and Rem. Sens., vol. 45, n. 8, pp. 2492-2500, August 2007

31. R. Persico, F. Soldovieri, Effects of the Background Removal in Linear Inverse Scattering, IEEE Trans. on Geos. and Rem. Sens., vol. 46, n. 4, pp. 1104-1114, April 2008.

32. G. Meles, S. Greenhalg, J. van der Kruk, A. Green, H. Maurer, “Taming the non-linearity problem in GPR full-waveform inversion fo high contrast media, Journal of Applied Geophysics, vol. 73, n. 2, pp. 174-186, 2011.