GPR Imaging Via Qualitative and Quantitative Approaches

  • Ilaria CatapanoEmail author
  • Andrea Randazzo
  • Evert Slob
  • Raffaele Solimene
Part of the Springer Transactions in Civil and Environmental Engineering book series (STICEE)


Ground Penetrating Radar (GPR) is a non-destructive imaging system able to provide high-resolution images of the subsurface. From a theoretical point of view, it requires to solve an inverse scattering problem, where a set of parameters describing the underground scenario must be retrieved starting from samples of the measured electromagnetic field. In this chapter, an overview of different methods/algorithms for quantitative and qualitative buried scatterer reconstruction widespread in literature is provided.


Ground Penetrating Radar Factorization Method Synthetic Aperture Radar Imaging Scattered Field Contrast Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work is a contribution to COST Action TU1208 “Civil Engineering Applications of Ground Penetrating Radar”.


  1. Abubaker, A., Van Den Berg, P.M.: Total variation as a multiplicative constraint for solving inverse problems. IEEE Trans. Image Process. 10, 1384–1392 (2001). doi: 10.1109/83.941862 CrossRefGoogle Scholar
  2. Abubakar, A., Habashy, T.M., Pan, G., Li, M.-K.: Application of the multiplicative regularized gauss-newton algorithm for three-dimensional microwave imaging. IEEE Trans. Antennas Propag. 60, 2431–2441 (2012). doi: 10.1109/TAP.2012.2189712 MathSciNetCrossRefGoogle Scholar
  3. Agarwal, K., Chen, X., Zhong, Y.: A multipole-expansion based linear sampling method for solving inverse scattering problems. Opt. Express 18, 6366 (2010). doi: 10.1364/OE.18.006366 CrossRefGoogle Scholar
  4. Ahmad, F., Amin, M.G., Kassam, S.A.: Synthetic aperture beamformer for imaging through a dielectric wall. IEEE Trans. Aerosp. Electron. Syst. 41, 271–283 (2005). doi: 10.1109/TAES.2005.1413761 CrossRefGoogle Scholar
  5. Ali, M.A., Moghaddam, M.: 3D nonlinear super-resolution microwave inversion technique using time-domain data. IEEE Trans. Antennas Propag. 58, 2327–2336 (2010). doi: 10.1109/TAP.2010.2048848 MathSciNetCrossRefGoogle Scholar
  6. Ammari, H., Iakovleva, E., Lesselier, D.: A MUSIC algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency. Multiscale Model. Simul. 3, 597–628 (2005). doi: 10.1137/040610854 MathSciNetCrossRefzbMATHGoogle Scholar
  7. Anyong, Q.: Electromagnetic inverse scattering of multiple two-dimensional perfectly conducting objects by the differential evolution strategy. IEEE Trans. Antennas Propag. 51, 1251–1262 (2003). doi: 10.1109/TAP.2003.811492 CrossRefGoogle Scholar
  8. Aramini, R., Brignone, M., Piana, M.: The linear sampling method without sampling. Inverse Probl. 22, 2237–2254 (2006). doi: 10.1088/0266-5611/22/6/020 MathSciNetCrossRefzbMATHGoogle Scholar
  9. Aramini, R., Caviglia, G., Massa, A., Piana, M.: The linear sampling method and energy conservation. Inverse Probl. 26, 055004 (2010). doi: 10.1088/0266-5611/26/5/055004 MathSciNetCrossRefGoogle Scholar
  10. Aramini, R., Brignone, M., Caviglia, G., et al.: The linear sampling method in a lossy background: an energy perspective. Inverse Probl Sci. Eng. 19, 963–984 (2011). doi: 10.1080/17415977.2011.565875 CrossRefzbMATHGoogle Scholar
  11. Arens, T.: Why linear sampling works. Inverse Probl. 20, 163–173 (2004). doi: 10.1088/0266-5611/20/1/010 MathSciNetCrossRefzbMATHGoogle Scholar
  12. Arens, T., Lechleiter, A.: The linear sampling method revisited. J. Integral Equ. Appl. 21, 179–202 (2009). doi: 10.1216/JIE-2009-21-2-179 MathSciNetCrossRefzbMATHGoogle Scholar
  13. Azaro, R., Bozza, G., Estatico, C., et al.: New results on electromagnetic imaging based on the inversion of synthetic and measured scattered-field data. IEEE Trans. Instrum. Meas. 55, 1085–1093 (2006). doi: 10.1109/TIM.2006.876576 CrossRefGoogle Scholar
  14. Baraniuk, R.: Compressive sensing. IEEE Signal Process. Mag. 24, 118–121 (2007). doi: 10.1109/MSP.2007.4286571 CrossRefGoogle Scholar
  15. Baranoski, E.J.: Through-wall imaging: historical perspective and future directions. J. Frankl Inst. 345, 556–569 (2008). doi: 10.1016/j.jfranklin.2008.01.005 CrossRefzbMATHGoogle Scholar
  16. Baussard, A., Miller, E.L., Lesselier, D.: Adaptive multiscale reconstruction of buried objects. Inverse Probl. 20, S1–S15 (2004a). doi: 10.1088/0266-5611/20/6/S01 CrossRefGoogle Scholar
  17. Baussard, A., Miller, E.L., Prémel, D.: Adaptive B-spline scheme for solving an inverse scattering problem. Inverse Probl. 20, 347–365 (2004b). doi: 10.1088/0266-5611/20/2/003 CrossRefzbMATHGoogle Scholar
  18. Belkebir, K., Bonnard, S., Pezin, F., et al.: Validation of 2D inverse scattering algorithms from multi-frequency experimental data. J. Electromagn. Waves Appl. 14, 1637–1667 (2000). doi: 10.1163/156939300X00437 CrossRefzbMATHGoogle Scholar
  19. Benedetti, M., Donelli, M., Martini, A., et al.: An innovative microwave-imaging technique for nondestructive evaluation: applications to civil structures monitoring and biological bodies inspection. IEEE Trans. Instrum. Meas. 55, 1878–1884 (2006). doi: 10.1109/TIM.2006.884287 CrossRefGoogle Scholar
  20. Berkhout, A.J.: Seismic inversion in terms of pre-stack migration and multiple elimination. Proc. IEEE 74, 415–427 (1986). doi: 10.1109/PROC.1986.13483 CrossRefGoogle Scholar
  21. Bermani, E., Boni, A., Caorsi, S., Massa, A.: An innovative real-time technique for buried object detection. IEEE Trans. Geosci. Remote Sens. 41, 927–931 (2003). doi: 10.1109/TGRS.2003.810928 CrossRefGoogle Scholar
  22. Bertero, M.: Linear inverse and ill-posed problems. In: Kazan, B. (ed.) Advances in Electronics and Electron Physics, vol. 75, pp. 1–120 (1989)Google Scholar
  23. Bertero, M., Boccacci, P.: Introduction to Inverse Problems in Imaging. IOP Publishing, Bristol (1998)CrossRefzbMATHGoogle Scholar
  24. Bevan, M.J., Endres, A.L., Rudolph, D.L., Parkin, G.: The non-invasive characterization of pumping-induced dewatering using ground penetrating radar. J. Hydrol. 281, 55–69 (2003). doi: 10.1016/S0022-1694(03)00200-2 CrossRefGoogle Scholar
  25. Bleistein, N.: Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion. Springer, New York (2001)CrossRefzbMATHGoogle Scholar
  26. Bloemenkamp, R.F., Slob, E.C.: Imaging of high-frequency fullvectorial GPR data using measured footprints: 23rd IEEE Geoscience and Remote Sensing Symposium IGARS, 1362–1364 (2003)Google Scholar
  27. Blum, C., Merkle, D.: Swarm Intelligence Introduction and Applications. Springer, Berlin (2008)CrossRefzbMATHGoogle Scholar
  28. Bozza, G., Pastorino, M.: An inexact newton-based approach to microwave imaging within the contrast source formulation. IEEE Trans. Antennas Propag. 57, 1122–1132 (2009). doi: 10.1109/TAP.2009.2015820 CrossRefGoogle Scholar
  29. Bozza, G., Estatico, C., Pastorino, M., Randazzo, A.: An inexact newton method for microwave reconstruction of strong scatterers. IEEE Antennas Wirel. Propag. Lett. 5, 61–64 (2006). doi: 10.1109/LAWP.2006.870360 CrossRefGoogle Scholar
  30. Bozza, G., Estatico, C., Massa, A., et al.: Short-range image-based method for the inspection of strong scatterers using microwaves. IEEE Trans. Instrum. Meas. 56, 1181–1188 (2007). doi: 10.1109/TIM.2007.900127 CrossRefGoogle Scholar
  31. Brandfass, M., Lanterman, A.D., Warnick, K.F.: A comparison of the Colton-Kirsch inverse scattering methods with linearized tomographic inverse scattering. Inverse Probl. 17, 1797–1816 (2001). doi: 10.1088/0266-5611/17/6/316 MathSciNetCrossRefzbMATHGoogle Scholar
  32. Breard, A., Perrusson, G., Lesselier, D.: Hybrid differential evolution and retrieval of buried spheres in subsoil. IEEE Geosci. Remote Sens. Lett. 5, 788–792 (2008). doi: 10.1109/LGRS.2008.2005790 CrossRefGoogle Scholar
  33. Brignone, M., Bozza, G., Randazzo, A., et al.: A hybrid approach to 3D microwave imaging by using linear sampling and ACO. IEEE Trans. Antennas Propag. 56, 3224–3232 (2008). doi: 10.1109/TAP.2008.929504 MathSciNetCrossRefGoogle Scholar
  34. Brignone, M., Bozza, G., Aramini, R., et al.: A fully no-sampling formulation of the linear sampling method for three-dimensional inverse electromagnetic scattering problems. Inverse Probl. (2009). doi: 10.1088/0266-5611/25/1/015014 MathSciNetGoogle Scholar
  35. Bristow, C.S., Jol, H.M.: An introduction to ground penetrating radar (GPR) in sediments. Geol. Soc. Lond. Spec. Publ. 211, 1–7 (2003). doi: 10.1144/GSL.SP.2001.211.01.01 CrossRefGoogle Scholar
  36. Bucci, O.M., Franceschetti, G.: On the degrees of freedom of scattered fields. IEEE Trans. Antennas Propag. 37, 918–926 (1989). doi: 10.1109/8.29386 MathSciNetCrossRefzbMATHGoogle Scholar
  37. Bucci, O.M., Isernia, T.: Electromagnetic inverse scattering: retrievable information and measurement strategies. Radio Sci. 32, 2123–2137 (1997). doi: 10.1029/97RS01826 CrossRefGoogle Scholar
  38. Bucci, O.M., Gennarelli, C., Savarese, C.: Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples. IEEE Trans. Antennas Propag. 46, 351–359 (1998). doi: 10.1109/8.662654 CrossRefGoogle Scholar
  39. Bucci, O.M., Cardace, N., Crocco, L., Isernia, T.: Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems. J. Opt. Soc. Am. A: 18, 1832 (2001a). doi: 10.1364/JOSAA.18.001832 CrossRefGoogle Scholar
  40. Bucci, O.M., Crocco, L., Isernia, T., Pascazio, V.: Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information. IEEE Trans. Geosci. Remote Sens. 39, 2527–2538 (2001b). doi: 10.1109/36.964991 CrossRefGoogle Scholar
  41. Busch, S., van der Kruk, J., Bikowski, J., Vereecken, H.: Quantitative conductivity and permittivity estimation using full-waveform inversion of on-ground GPR data. Geophysics 77, H79–H91 (2012). doi: 10.1190/geo2012-0045.1 CrossRefGoogle Scholar
  42. Cafforio, C., Prati, C., Rocca, F.: SAR data focusing using seismic migration techniques. IEEE Trans. Aerosp. Electron. Syst. 27, 194–207 (1991). doi: 10.1109/7.78293 CrossRefGoogle Scholar
  43. Cakoni, F.: Qualitative Methods in Inverse Scattering Theory: An Introduction. Springer, Berlin (2006)Google Scholar
  44. Caorsi, S., Pastorino, M.: Two-dimensional microwave imaging approach based on a genetic algorithm. IEEE Trans. Antennas Propag. 48, 370–373 (2000). doi: 10.1109/8.841897 CrossRefGoogle Scholar
  45. Caorsi, S., Gragnani, G.L., Medicina, S., et al.: Microwave imaging based on a Markov random field model. IEEE Trans. Antennas Propag. 42, 293–303 (1994). doi: 10.1109/8.280714 CrossRefGoogle Scholar
  46. Caorsi, S., Ciaramella, S., Gragnani, G.L., Pastorino, M.: On the use of regularization techniques in numerical inverse-scattering solutions for microwave imaging applications. IEEE Trans. Microw. Theory Tech. 43, 632–640 (1995). doi: 10.1109/22.372110 CrossRefGoogle Scholar
  47. Caorsi, S., Pastorino, M., Raffetto, M.: Electromagnetic scattering by a multilayer elliptic cylinder under transverse-magnetic illumination: series solution in terms of Mathieu functions. IEEE Trans. Antennas Propag. 45, 926–935 (1997). doi: 10.1109/8.585739 CrossRefGoogle Scholar
  48. Caorsi, S., Massa, A., Pastorino, M.: A computational technique based on a real-coded genetic algorithm for microwave imaging purposes. IEEE Trans. Geosci. Remote Sens. 38, 1697–1708 (2000). doi: 10.1109/36.851968 CrossRefGoogle Scholar
  49. Caorsi, S., Costa, A., Pastorino, M.: Microwave imaging within the second-order Born approximation: stochastic optimization by a genetic algorithm. IEEE Trans. Antennas Propag. 49, 22–31 (2001a). doi: 10.1109/8.910525 CrossRefzbMATHGoogle Scholar
  50. Caorsi, S., Massa, A., Pastorino, M.: A crack identification microwave procedure based on a genetic algorithm for nondestructive testing. IEEE Trans. Antennas Propag. 49, 1812–1820 (2001b). doi: 10.1109/8.982464 CrossRefGoogle Scholar
  51. Caorsi, S., Donelli, M., Franceschini, D., Massa, A.: A new methodology based on an iterative multiscaling for microwave imaging. IEEE Trans. Microw. Theory Tech. 51, 1162–1173 (2003a). doi: 10.1109/TMTT.2003.809677 CrossRefGoogle Scholar
  52. Caorsi, S., Massa, A., Pastorino, M., et al.: Detection of buried inhomogeneous elliptic cylinders by a memetic algorithm. IEEE Trans. Antennas Propag. 51, 2878–2884 (2003b). doi: 10.1109/TAP.2003.817984 CrossRefGoogle Scholar
  53. Caorsi, S., Massa, A., Pastorino, M., Randazzo, A.: Electromagnetic detection of dielectric scatterers using phaseless synthetic and real data and the memetic algorithm. IEEE Trans. Geosci. Remote Sens. 41, 2745–2753 (2003c). doi: 10.1109/TGRS.2003.815676 CrossRefGoogle Scholar
  54. Caorsi, S., Donelli, M., Lommi, A., Massa, A.: Location and imaging of two-dimensional scatterers by using a particle swarm algorithm. J. Electromagn. Waves Appl. 18, 481–494 (2004). doi: 10.1163/156939304774113089 MathSciNetCrossRefGoogle Scholar
  55. Catapano, I., Crocco, L., Isernia,T.: A simple two-dimensional inversion technique for imaging homogeneous targets in stratified media: inverse scattering in stratified media. Radio Sci. 39, RS1012 (2004). doi:  10.1029/2003RS002917
  56. Catapano, I., Crocco, L., D’Urso, M., Isernia, T.: A novel effective model for solving 3-d nonlinear inverse scattering problems in lossy scenarios. IEEE Geosci. Remote Sens. Lett. 3, 302–306 (2006a). doi: 10.1109/LGRS.2006.869976 CrossRefGoogle Scholar
  57. Catapano, I., Crocco, L., Persico, R., et al.: Linear and nonlinear microwave tomography approaches for subsurface prospecting: validation on real data. Antennas Wirel Propag. Lett. 5, 49–53 (2006b). doi: 10.1109/LAWP.2006.870363 CrossRefGoogle Scholar
  58. Catapano, I., Crocco, L., Isernia, T.: On simple methods for shape reconstruction of unknown scatterers. IEEE Trans. Antennas Propag. 55, 1431–1436 (2007). doi: 10.1109/TAP.2007.895563 CrossRefGoogle Scholar
  59. Catapano, I., Crocco, L., Isernia, T.: improved sampling methods for shape reconstruction of 3-D buried targets. IEEE Trans. Geosci. Remote Sens. 46, 3265–3273 (2008). doi: 10.1109/TGRS.2008.921745 CrossRefGoogle Scholar
  60. Catapano, I., Crocco, L., Urso, M.D., Isernia, T.: 3D microwave imaging via preliminary support reconstruction: testing on the Fresnel 2008 database. Inverse Probl. 25, 024002 (2009). doi: 10.1088/0266-5611/25/2/024002 CrossRefGoogle Scholar
  61. Catapano, I., Crocco, L.: A qualitative inverse scattering method for through-the-wall imaging. IEEE Geosci. Remote Sens.Lett. 7, 685–689 (2010). doi: 10.1109/LGRS.2010.2045473 CrossRefGoogle Scholar
  62. Catapano, I., Soldovieri, F., Crocco, L.: On the feasibility of the linear sampling method for 3d Gpr surveys. Prog. Electromagn. Res. 118, 185–203 (2011). doi: 10.2528/PIER11042704 CrossRefGoogle Scholar
  63. Catapano, I., Crocco, L., Napoli, R.D., et al.: Microwave tomography enhanced GPR surveys in Centaur’s Domus, Regio VI of Pompeii, Italy. J. Geophys. Eng. 9, S92–S99 (2012). doi: 10.1088/1742-2132/9/4/S92 CrossRefGoogle Scholar
  64. Chen, W.-T., Chiu, C.-C.: Electromagnetic imaging for an imperfectly conducting cylinder by the genetic algorithm. IEEE Trans. Microw. Theory Tech. 48, 1901–1905 (2000). doi: 10.1109/22.883869 CrossRefGoogle Scholar
  65. Cheney, M.: The linear sampling method and the MUSIC algorithm. Inverse Probl. 17, 591–595 (2001). doi: 10.1088/0266-5611/17/4/301 MathSciNetCrossRefzbMATHGoogle Scholar
  66. Chew, W.C.: Waves and Fields in Inhomogeneous Media. IEEE Press, London (1999)Google Scholar
  67. Chew, W.C., Wang, Y.M.: Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method. IEEE Trans. Med. Imaging 9, 218–225 (1990). doi: 10.1109/42.56334 CrossRefGoogle Scholar
  68. Chew, W.C., Lin, J.H.: A frequency-hopping approach for microwave imaging of large inhomogeneous bodies. IEEE Microw. Guid. Wave Lett. 5, 439–441 (1995). doi: 10.1109/75.481854 CrossRefGoogle Scholar
  69. Chiu, C.-C., Liu, P.-T.: Image reconstruction of a perfectly conducting cylinder by the genetic algorithm. IEE Proc.—Microw. Antennas Propag. 143, 249 (1996). doi: 10.1049/ip-map:19960363 CrossRefGoogle Scholar
  70. Clerc, M.: Particle Swarm Optimization. ISTE, New Delhi (2006)Google Scholar
  71. Collino, F., Fares, M.B., Haddar, H.: Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems. Inverse Probl. 19, 1279–1298 (2003). doi: 10.1088/0266-5611/19/6/004 MathSciNetCrossRefzbMATHGoogle Scholar
  72. Colton, D., Kirsch, A.: A simple method for solving inverse scattering problems in the resonance region. Inverse Probl. 12, 383–393 (1996). doi: 10.1088/0266-5611/12/4/003 MathSciNetCrossRefzbMATHGoogle Scholar
  73. Colton, D., Piana, M., Potthast, R.: A simple method using Morozov’s discrepancy principle for solving inverse scattering problems. Inverse Probl. 13, 1477–1493 (1997). doi: 10.1088/0266-5611/13/6/005 MathSciNetCrossRefzbMATHGoogle Scholar
  74. Colton, D., Giebermann, K., Monk, P.: A regularized sampling method for solving three-dimensional inverse scattering problems. SIAM J. Sci. Comput. 21, 2316–2330 (2000). doi: 10.1137/S1064827598340159 MathSciNetCrossRefzbMATHGoogle Scholar
  75. Colton, D., Haddar, H., Piana, M.: The linear sampling method in inverse electromagnetic scattering theory. Inverse Probl. 19, S105–S137 (2003). doi: 10.1088/0266-5611/19/6/057 MathSciNetCrossRefzbMATHGoogle Scholar
  76. Conyers, L.B.: Ground-Penetrating Radar: An Introduction for Archaeologists. AltaMira Press, Walnut Creek (1997)Google Scholar
  77. Counts, T., Gurbuz, A.C., Scott, W.R., et al.: Multistatic ground-penetrating radar experiments. IEEE Trans. Geosci. Remote Sens. 45, 2544–2553 (2007). doi: 10.1109/TGRS.2007.900677 CrossRefGoogle Scholar
  78. Coyle, J.: Locating the support of objects contained in a two-layered background medium in two dimensions. Inverse Probl. 16, 275–292 (2000). doi: 10.1088/0266-5611/16/2/301 MathSciNetCrossRefzbMATHGoogle Scholar
  79. Crocco, L., D’Urso, M., Isernia, T.: Testing the contrast source extended Born inversion method against real data: the TM case. Inverse Probl. 21, S33–S50 (2005). doi: 10.1088/0266-5611/21/6/S04 MathSciNetCrossRefzbMATHGoogle Scholar
  80. Crocco L., Soldovieri, F.: Nonlinear Inversion Algorithms. Subsurf. Sens. 1, 365–376 (2011)Google Scholar
  81. Crocco, L., Catapano, I., Di Donato, L., Isernia, T.: The linear sampling method as a way to quantitative inverse scattering. IEEE Trans. Antennas Propag. 60, 1844–1853 (2012). doi: 10.1109/TAP.2012.2186250 CrossRefGoogle Scholar
  82. Cui, T.J., Chew, W.C., Aydiner, A.A., Chen, S.: Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method. IEEE Trans. Geosci. Remote Sens. 39, 339–346 (2001). doi: 10.1109/36.905242 CrossRefGoogle Scholar
  83. D’Urso, M., Catapano, I., Crocco, L., Isernia, T.: Effective solution of 3-D scattering problems via series expansions: applicability and a new hybrid scheme. IEEE Trans. Geosci. Remote Sens. 45, 639–648 (2007). doi: 10.1109/TGRS.2006.888144 CrossRefGoogle Scholar
  84. D’Urso, M., Isernia, T., Morabito, A.F.: On the solution of 2-D inverse scattering problems via source-type integral equations. IEEE Trans. Geosci. Remote Sens. 48, 1186–1198 (2010). doi: 10.1109/TGRS.2009.2032175 CrossRefGoogle Scholar
  85. Daniels, D.J.: Ground Penetrating Radar, 2nd edn. Institution of Electrical Engineers, London (2004)CrossRefGoogle Scholar
  86. Devaney, A.J.: Super-resolution processing of multi-static data using time reversal And MUSIC. Northeastern University (2000)Google Scholar
  87. De Micheli, E., Magnoli, N., Viano, G.A.: On the regularization of fredholm integral equations of the first kind. SIAM J. Math. Anal. 29, 855–877 (1998). doi: 10.1137/S0036141096301749 MathSciNetCrossRefzbMATHGoogle Scholar
  88. De Micheli, E., Viano, G.A.: Metric and probabilistic information associated with fredholm integral equations of the first kind. J. Integral Equ. Appl. 14, 283–310 (2002). doi: 10.1216/jiea/1181074917 CrossRefzbMATHGoogle Scholar
  89. De Zaeytijd, J., Franchois, A., Eyraud, C., Geffrin, J.-M.: Full-wave three-dimensional microwave imaging with a regularized gauss-newton method—theory and experiment. IEEE Trans. Antennas Propag. 55, 3279–3292 (2007). doi: 10.1109/TAP.2007.908824 CrossRefGoogle Scholar
  90. Di Matteo, A., Pettinelli, E., Slob, E.: Early-time GPR signal attributes to estimate soil dielectric permittivity: a theoretical study. IEEE Trans. Geosci. Remote Sens. 51, 1643–1654 (2013). doi: 10.1109/TGRS.2012.2206817 CrossRefGoogle Scholar
  91. Di Vico, M., Frezza, F., Pajewski, L., Schettini, G.: Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution. IEEE Trans. Antennas Propag. 53, 719–727 (2005). doi: 10.1109/TAP.2004.841315 CrossRefGoogle Scholar
  92. Donelli, M., Franceschini, G., Martini, A., Massa, A.: An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems. IEEE Trans. Geosci. Remote Sens. 44, 298–312 (2006). doi: 10.1109/TGRS.2005.861412 CrossRefGoogle Scholar
  93. Donelli, M., Craddock, I., Gibbins, D., Sarafianou, M.: A three-dimensional time domain microwave imaging method for breast cancer detection based on an evolutionary algorithm. Prog. Electromagn. Res. M 18, 179–195 (2011)CrossRefGoogle Scholar
  94. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289–1306 (2006). doi: 10.1109/TIT.2006.871582 MathSciNetCrossRefzbMATHGoogle Scholar
  95. Dourthe, C., Pichot, C., Dauvignac, J.Y., Cariou, J.: Inversion algorithm and measurement system for microwave tomography of buried object. Radio Sci. 35, 1097–1108 (2000). doi: 10.1029/1999RS002244 CrossRefGoogle Scholar
  96. Ernst, J.R., Maurer, H., Green, A.G., Holliger, K.: Full-waveform inversion of crosshole radar data based on 2-D finite-difference time-domain solutions of Maxwell’s equations. IEEE Trans. Geosci. Remote Sens. 45, 2807–2828 (2007). doi: 10.1109/TGRS.2007.901048 CrossRefGoogle Scholar
  97. Estatico, C., Pastorino, M., Randazzo, A.: An inexact-Newton method for short-range microwave imaging within the second-order Born approximation. IEEE Trans. Geosci. Remote Sens. 43, 2593–2605 (2005). doi: 10.1109/TGRS.2005.856631 CrossRefGoogle Scholar
  98. Estatico, C., Pastorino, M., Randazzo, A.: A novel microwave imaging approach based on regularization in Lp Banach spaces. IEEE Trans. Antennas Propag. 60, 3373–3381 (2012). doi: 10.1109/TAP.2012.2196925 MathSciNetCrossRefGoogle Scholar
  99. Estatico, C., Fedeli, A., Pastorino, M., Randazzo, A.: Microwave imaging of elliptically shaped dielectric cylinders by means of an Lp Banach-space inversion algorithm. Meas. Sci. Technol. 24, 074017 (2013). doi: 10.1088/0957-0233/24/7/074017 CrossRefGoogle Scholar
  100. Fink, M.: Time reversal of ultrasonic fields. I. Basic principles. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 555–566 (1992). doi: 10.1109/58.156174 CrossRefGoogle Scholar
  101. Fischer, C., Herschlein, A., Younis, M., Wiesbeck, W.: Detection of antipersonnel mines by using the factorization method on multistatic ground-penetrating radar measurements. IEEE Trans. Geosci. Remote Sens. 45, 85–92 (2007). doi: 10.1109/TGRS.2006.883464 CrossRefGoogle Scholar
  102. Franchois, A., Pichot, C.: Microwave imaging-complex permittivity reconstruction with a Levenberg-Marquardt method. IEEE Trans. Antennas Propag. 45, 203–215 (1997). doi: 10.1109/8.560338 CrossRefGoogle Scholar
  103. Frezza, F., Martinelli, P., Pajewski, L., Schettini, G.: Short-pulse electromagnetic scattering by buried perfectly conducting cylinders. IEEE Geosci. Remote Sens. Lett. 4, 611–615 (2007). doi: 10.1109/LGRS.2007.903078 CrossRefGoogle Scholar
  104. Gamba, P., Lossani, S.: Neural detection of pipe signatures in ground penetrating radar images. IEEE Trans. Geosci. Remote Sens. 38, 790–797 (2000). doi: 10.1109/36.842008 CrossRefGoogle Scholar
  105. Gazdag, J.: Wave equation migration with the phase shift method: Geophysics, 43, 1342–1351 (1978)Google Scholar
  106. Gazdag, J., Sguazzero, P.: Migration of seismic data. Proc. IEEE 72, 1302–1315 (1984). doi: 10.1109/PROC.1984.13019 CrossRefGoogle Scholar
  107. Gebauer, B., Hanke, M., Kirsch, A., et al.: A sampling method for detecting buried objects using electromagnetic scattering. Inverse Probl. 21, 2035–2050 (2005). doi: 10.1088/0266-5611/21/6/015 MathSciNetCrossRefzbMATHGoogle Scholar
  108. Gilmore, C., Jeffrey, I., LoVetri, J.: Derivation and comparison of SAR and frequency-wavenumber migration within a common inverse scalar wave problem formulation. IEEE Trans. Geosci. Remote Sens. 44, 1454–1461 (2006). doi: 10.1109/TGRS.2006.870402 CrossRefGoogle Scholar
  109. Gorriti, A.G., Slob, E.C.: A new tool for accurate S-parameters measurements and permittivity reconstruction. IEEE Trans. Geosci. Remote Sens. 43, 1727–1735 (2005). doi: 10.1109/TGRS.2005.851163 CrossRefGoogle Scholar
  110. Groetsch, C.W.: Inverse Problems in the Mathematical Sciences. Vieweg, Braunschweig (1993)CrossRefzbMATHGoogle Scholar
  111. Guzina, B.B., Cakoni, F., Bellis, C.: On the multi-frequency obstacle reconstruction via the linear sampling method. Inverse Probl. 26, 125005 (2010). doi: 10.1088/0266-5611/26/12/125005 MathSciNetCrossRefGoogle Scholar
  112. Hagedoorn, J.G.: A process of seismic reflection interpretation. Geophys. Prospect. 2, 85–127 (1954). doi: 10.1111/j.1365-2478.1954.tb01281.x CrossRefGoogle Scholar
  113. Hansen, P.C., Nagy, J.G., O’Leary, D.P.: Deblurring Images: Mmatrices, Spectra, and Filtering. SIAM, Philadelphia (2006)CrossRefGoogle Scholar
  114. Hansen, T.B., Johansen, P.M.: Inversion scheme for ground penetrating radar that takes into account the planar air-soil interface. IEEE Trans. Geosci. Remote Sens. 38, 496–506 (2000). doi: 10.1109/36.823944 CrossRefGoogle Scholar
  115. Harada, H., Wall, D.J.N., Takenaka, T., Tanaka, M.: Conjugate Gradient method applied to inverse scattering problem. IEEE Trans. Antennas Propag. 43, 784–792 (1995). doi: 10.1109/8.402197 CrossRefGoogle Scholar
  116. Haupt, R.L.: An introduction to genetic algorithms for electromagnetics. IEEE Antennas Propag. Mag. 37, 7–15 (1995). doi: 10.1109/74.382334 CrossRefGoogle Scholar
  117. Huang, C.-H., Chiu, C.-C., Li, C.-L., Chen, K.-C.: Time domain inverse scattering of a two-dimensional homogenous dielectric object with arbitrary shape by particle swarm optimization. Prog Electromagn Res. 82, 381–400 (2008). doi: 10.2528/PIER08031904 CrossRefGoogle Scholar
  118. Huang, T., Mohan, A.S.: A Microparticle swarm optimizer for the reconstruction of microwave images. IEEE Trans. Antennas Propag. 55, 568–576 (2007). doi: 10.1109/TAP.2007.891545 CrossRefGoogle Scholar
  119. Hugenschmidt, J., Kalogeropoulos, A.: The inspection of retaining walls using GPR. J. Appl. Geophys. 67, 335–344 (2009). doi: 10.1016/j.jappgeo.2008.09.001 CrossRefGoogle Scholar
  120. Huisman, J.A., Hubbard, S.S., Redman, J.D., Annan, A.P.: Measuring soil water content with ground penetrating radar: a review. Vadose Zone J. 2, 476–491 (2003). doi: 10.2113/2.4.476 CrossRefGoogle Scholar
  121. Ikehata, M.: Reconstruction of an obstacle from the scattering amplitude at a fixed frequency. Inverse Probl. 14, 949–954 (1998). doi: 10.1088/0266-5611/14/4/012 MathSciNetCrossRefzbMATHGoogle Scholar
  122. Isernia, T., Pascazio, V., Pierri, R.: A nonlinear estimation method in tomographic imaging. IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997). doi: 10.1109/36.602533 CrossRefGoogle Scholar
  123. Isernia, T., Pascazio, V., Pierri, R.: On the local minima in a tomographic imaging technique. IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001). doi: 10.1109/36.934091 CrossRefGoogle Scholar
  124. Isernia, T., Crocco, L., D’Urso, M.: New tools and series for forward and inverse scattering problems in Lossy media. IEEE Geosci. Remote Sens. Lett. 1, 327–331 (2004). doi: 10.1109/LGRS.2004.837008 CrossRefGoogle Scholar
  125. Jadoon, K.Z., Lambot, S., Slob, E.C., Vereecken, H.: Analysis of Horn antenna transfer functions and phase-center position for modeling off-ground GPR. IEEE Trans. Geosci. Remote Sens. 49, 1649–1662 (2011). doi: 10.1109/TGRS.2010.2089691 CrossRefGoogle Scholar
  126. Jang, H., Kuroda, S., Kim, H.J.: SVD inversion of zero-offset profiling data obtained in the Vadose Zone using cross-borehole radar. IEEE Trans. Geosci. Remote Sens. 49, 3849–3855 (2011). doi: 10.1109/TGRS.2011.2134855 CrossRefGoogle Scholar
  127. Kirsch, A.: Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Inverse Probl. 14, 1489–1512 (1998). doi: 10.1088/0266-5611/14/6/009 MathSciNetCrossRefzbMATHGoogle Scholar
  128. Kirsch, A.: Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory. Inverse Probl. 15, 413–429 (1999). doi: 10.1088/0266-5611/15/2/005 MathSciNetCrossRefzbMATHGoogle Scholar
  129. Kirsch, A.: The factorization method for Maxwell’s equations. Inverse Probl. 20, S117–S134 (2004). doi: 10.1088/0266-5611/20/6/S08 MathSciNetCrossRefzbMATHGoogle Scholar
  130. Kleinman, R.E., van den Berg, P.M.: A modified gradient method for two- dimensional problems in tomography. J. Comput. Appl. Math. 42, 17–35 (1992). doi: 10.1016/0377-0427(92)90160-Y MathSciNetCrossRefzbMATHGoogle Scholar
  131. Klotzsche, A., Van der Kruk, J., Meles, G.A., et al.: Full-waveform inversion of cross-hole ground-penetrating radar data to characterize a gravel aquifer close to the Thur River, Switzerland. Surf. Geophys. 8, 631–646 (2010). doi: 10.3997/1873-0604.2010054 Google Scholar
  132. Krasnov, M.L., Kiselev, A.I., Makarenko, G.I.: Integral Equations. MIR, Moscow (1976)Google Scholar
  133. Lambot, S., Slob, E.C., van den Bosch, I., et al.: Modeling of ground-penetrating Radar for accurate characterization of subsurface electric properties. IEEE Trans. Geosci. Remote Sens. 42, 2555–2568 (2004). doi: 10.1109/TGRS.2004.834800 CrossRefGoogle Scholar
  134. Lambot, S., André, F.: Full-wave modeling of near-field radar data for planar layered media reconstruction. IEEE Trans. Geosci. Remote Sens. 52, 2295–2303 (2014). doi: 10.1109/TGRS.2013.2259243 CrossRefGoogle Scholar
  135. Langenberg, K.J.: Applied inverse problems for acoustic, electromagnetic and elastic wave scattering. In: Sabatier P.C. (ed.) Basic Methods of Tomography and Inverse Problems, pp. 127–467. Hilger, Bristol (1987)Google Scholar
  136. Leone, G., Persico, R., Solimene, R.: A quadratic model for electromagnetic subsurface prospecting. AEU—Int. J. Electron Commun. 57, 33–46 (2003). doi: 10.1078/1434-8411-54100138 CrossRefGoogle Scholar
  137. Li, F., Chen, X., Huang, K.: Microwave imaging a buried object by the GA and using the S11 parameter. Prog. Electromagn. Res. 85, 289–302 (2008). doi: 10.2528/PIER08081401 CrossRefGoogle Scholar
  138. Liseno, A., Pierri, R.: Shape reconstruction by the spectral data of the far-field operator: analysis and performances. IEEE Trans. Antennas Propag. 52, 899–903 (2004). doi: 10.1109/TAP.2004.824674 CrossRefGoogle Scholar
  139. Liu, Q.H., Zhang, Z.Q., Wang, T.T., et al.: Active microwave imaging. I. 2-D forward and inverse scattering methods. IEEE Trans. Microw. Theory Tech. 50, 123–133 (2002). doi: 10.1109/22.981256 CrossRefGoogle Scholar
  140. Lobel, P., Kleinman, R.E., Pichot, C., et al.: Conjugate-gradient method for solving inverse scattering with experimental data. IEEE Antennas Propag. Mag. 38, 48 (1996). doi: 10.1109/MAP.1996.511954 CrossRefGoogle Scholar
  141. Lobel, P., Blanc-Féraud, L., Pichot, C., Barlaud, M.: A new regularization scheme for inverse scattering. Inverse Probl. 13, 403 (1997). doi: 10.1088/0266-5611/13/2/013 CrossRefzbMATHGoogle Scholar
  142. Lopera, O., Milisavljević, N., Lambot, S.: Clutter reduction in GPR measurements for detecting shallow buried landmines: a Colombian case study. Surf. Geophys. 5, 57–64 (2007). doi: 10.3997/1873-0604.2006018 Google Scholar
  143. Lopez-Sahcnez, J.M., Fortuny-Guasch, J.: 3-D radar imaging using range migration techniques. IEEE Trans. Antennas Propag. 48, 728–737 (2000). doi: 10.1109/8.855491 CrossRefGoogle Scholar
  144. Luke, D.R., Potthast, R.: The no response test—a sampling method for inverse scattering problems. SIAM J Appl Math 63, 1292–1312 (2003). doi: 10.1137/S0036139902406887 MathSciNetCrossRefzbMATHGoogle Scholar
  145. Marengo, E.A., Gruber, F.K., Simonetti, F.: Time-reversal MUSIC imaging of extended targets. IEEE Trans. Image Process. 16, 1967–1984 (2007). doi: 10.1109/TIP.2007.899193 MathSciNetCrossRefGoogle Scholar
  146. Marklein, R., Mayer, K., Hannemann, R., et al.: Linear and nonlinear inversion algorithms applied in nondestructive evaluation. Inverse Probl. 18, 1733–1759 (2002). doi: 10.1088/0266-5611/18/6/319 MathSciNetCrossRefzbMATHGoogle Scholar
  147. Masini, N., Persico, R., Rizzo, E.: Some examples of GPR prospecting for monitoring of the monumental heritage. J. Geophys. Eng. 7, 190–199 (2010). doi: 10.1088/1742-2132/7/2/S05 CrossRefGoogle Scholar
  148. Masini, N., Soldovieri, F.: Integrated non-invasive sensing techniques and geophysical methods for the study and conservation of architectural, archaeological and artistic heritage. J. Geophys. Eng. (2011). doi: 10.1088/1742-2140/8/3/E01 Google Scholar
  149. Massa, A., Pastorino, M., Randazzo, A.: Reconstruction of two-dimensional buried objects by a differential evolution method. Inverse Probl. 20, S135–S150 (2004). doi: 10.1088/0266-5611/20/6/S09 CrossRefzbMATHGoogle Scholar
  150. Massa, A., Franceschini, D., Franceschini, G., et al.: Parallel GA-based approach for microwave imaging applications. IEEE Trans. Antennas Propag. 53, 3118–3127 (2005). doi: 10.1109/TAP.2005.856311 MathSciNetCrossRefGoogle Scholar
  151. Meles, G.A., Van der Kruk, J., Greenhalgh, S.A., et al.: A new vector waveform inversion algorithm for simultaneous updating of conductivity and permittivity parameters from combination crosshole/borehole-to-surface GPR Data. IEEE Trans. Geosci. Remote Sens. 48, 3391–3407 (2010). doi: 10.1109/TGRS.2010.2046670 CrossRefGoogle Scholar
  152. Meschino, S., Pajewski, L., Schettini, G.: A direction-of-arrival approach for the subsurface localization of a dielectric object. J. Appl. Geophys. 85, 68–79 (2012). doi: 10.1016/j.jappgeo.2012.07.002 CrossRefGoogle Scholar
  153. Meschino, S., Pajewski, L., Pastorino, M., et al.: Detection of subsurface metallic utilities by means of a sap technique: comparing MUSIC- and SVM-based approaches. J. Appl. Geophys. 97, 60–68 (2013). doi: 10.1016/j.jappgeo.2013.01.011 CrossRefGoogle Scholar
  154. Michalski, K.A.: Electromagnetic imaging of circular-cylindrical conductors and tunnels using a differential evolution algorithm. Microw. Opt. Technol. Lett. 27, 330–334 (2000). doi: 10.1002/1098-2760(20001205)27:5<330:AID-MOP13>3.0.CO;2-H CrossRefGoogle Scholar
  155. Michalski, K.A.: Electromagnetic imaging of elliptical-cylindrical conductors and tunnels using a differential evolution algorithm. Microw. Opt. Technol. Lett. 28, 164–169 (2001). doi: 10.1002/1098-2760(20010205)28:3<164:AID-MOP5>3.0.CO;2-D CrossRefGoogle Scholar
  156. Minet, J., Lambot, S., Slob, E.C., Vanclooster, M.: Soil surface water content estimation by full-waveform GPR signal inversion in the presence of thin layers. IEEE Trans. Geosci. Remote Sens. 48, 1138–1150 (2010). doi: 10.1109/TGRS.2009.2031907 CrossRefGoogle Scholar
  157. De Mol, C.: A critical survey of regularized inversion method. In: Bertero, M., Pike, E.R. (eds.) Inverse Problems in Scatterring Imaging, pp. 345–370. Hilger, Bristol (1992)Google Scholar
  158. Lo Monte, L., Erricolo, D., Soldovieri, F., Wicks, M.C.: Radio frequency tomography for tunnel detection. IEEE Trans. Geosci. Remote Sens. 48, 1128–1137 (2010). doi: 10.1109/TGRS.2009.2029341 CrossRefGoogle Scholar
  159. Mydur, R., Michalski, K.A.: A neural-network approach to the electromagnetic imaging of elliptic conducting cylinders. Microw Opt. Technol. Lett. 28, 303–306 (2001). doi: 10.1002/1098-2760(20010305)28:5<303:AID-MOP1024>3.0.CO;2-C CrossRefGoogle Scholar
  160. Neal, A.: Ground-penetrating radar and its use in sedimentology: principles, problems and progress. Earth-Sci. Rev. 66, 261–330 (2004). doi: 10.1016/j.earscirev.2004.01.004 CrossRefGoogle Scholar
  161. Oliveri, G., Lizzi, L., Pastorino, M., Massa, A.: A nested multi-scaling inexact-newton iterative approach for microwave imaging. IEEE Trans. Antennas Propag. 60, 971–983 (2012a). doi: 10.1109/TAP.2011.2173131 MathSciNetCrossRefGoogle Scholar
  162. Oliveri, G., Randazzo, A., Pastorino, M., Massa, A.: Electromagnetic imaging within the contrast-source formulation by means of the multiscaling inexact newton method. J. Opt. Soc. Am. A: 29, 945–958 (2012b). doi: 10.1364/JOSAA.29.000945 CrossRefGoogle Scholar
  163. Orlando, L., Soldovieri, F.: Two different approaches for georadar data processing: a case study in archaeological prospecting. J. Appl. Geophys. 64, 1–13 (2008). doi: 10.1016/j.jappgeo.2007.10.002 CrossRefGoogle Scholar
  164. Ostadrahimi, M., Mojabi, P., Zakaria, A., et al.: Enhancement of Gauss-Newton inversion method for biological tissue imaging. IEEE Trans. Microw. Theory Tech. 61, 3424–3434 (2013). doi: 10.1109/TMTT.2013.2273758 CrossRefGoogle Scholar
  165. Pastorino, M.: Short-range microwave inverse scattering techniques for image reconstruction and applications. IEEE Trans. Instrum. Meas. 47, 1419–1427 (1998). doi: 10.1109/19.746706 CrossRefGoogle Scholar
  166. Pastorino, M., Massa, A., Caorsi, S.: A microwave inverse scattering technique for image reconstruction based on a genetic algorithm. IEEE Trans. Instrum. Meas. 49, 573–578 (2000). doi: 10.1109/19.850397 CrossRefGoogle Scholar
  167. Pastorino, M., Caorsi, S., Massa, A., Randazzo, A.: Reconstruction algorithms for electromagnetic imaging. IEEE Trans. Instrum. Meas. 53, 692–699 (2004). doi: 10.1109/TIM.2004.827093 CrossRefGoogle Scholar
  168. Pastorino, M.: Stochastic optimization methods applied to microwave imaging: a review. IEEE Trans. Antennas Propag. 55, 538–548 (2007). doi: 10.1109/TAP.2007.891568 CrossRefGoogle Scholar
  169. Pastorino, M.: Microwave Imaging. Wiley, Hoboken (2010)Google Scholar
  170. Pastorino, M., Randazzo, A.: Buried object detection by an inexact-newton method applied to nonlinear inverse scattering. Int J. Microw. Sci. Technol. 2012, 1–7 (637301) (2012)Google Scholar
  171. Pastorino, M., Randazzo, A.: Nondestructive analysis of dielectric bodies by means of an ant colony optimization method. In: Fornarelli, G., Mescia, L. (eds.) Swarm Intelligence for Electric and Electronic Engineering, pp 308–325. Engineering Science Reference, Hershey, PA (2013). doi: 10.4018/978-1-4666-2666-9
  172. Patriarca, C., Lambot, S., Mahmoudzadeh, M.R., et al.: Reconstruction of sub-wavelength fractures and physical properties of masonry media using full-waveform inversion of proximal penetrating radar. J. Appl. Geophys. 74, 26–37 (2011). doi: 10.1016/j.jappgeo.2011.03.001 CrossRefGoogle Scholar
  173. Patriarca, C., Miorali, M., Slob, E., Lambot, S.: Uncertainty quantification in off-ground monostatic ground penetrating radar. IEEE Trans. Antennas Propag. 61, 3334–3344 (2013). doi: 10.1109/TAP.2013.2251597 CrossRefGoogle Scholar
  174. Persico, R., Bernini, R., Soldovieri, F.: The role of the measurement configuration in inverse scattering from buried objects under the Born approximation. IEEE Trans. Antennas Propag. 53, 1875–1887 (2005). doi: 10.1109/TAP.2005.848468 CrossRefGoogle Scholar
  175. Persico, R.: On the role of measurement configuration in contactless GPR data processing by means of linear inverse scattering. IEEE Trans. Antennas Propag. 54, 2062–2071 (2006). doi: 10.1109/TAP.2006.877170 CrossRefGoogle Scholar
  176. Pierri, R., Liseno, A., Solimene, R., Soldovieri, F.: Beyond physical optics SVD shape reconstruction of metallic cylinders. IEEE Trans. Antennas Propag. 54, 655–665 (2006). doi: 10.1109/TAP.2005.863121 CrossRefGoogle Scholar
  177. Pike, E.R., Sabatier, P.C.: Scattering: Scattering and Inverse Scattering in Pure and Applied Science. Academic Press, San Diego (2002)Google Scholar
  178. Piro, S., Goodman, D., Nishimura, Y.: The study and characterization of Emperor Traiano’s Villa (Altopiani di Arcinazzo, Roma) using high-resolution integrated geophysical surveys. Archaeol. Prospect. 10, 1–25 (2003). doi: 10.1002/arp.203 CrossRefGoogle Scholar
  179. Porsani, J.L., Filho, W.M., Elis, V.R., et al.: The use of GPR and VES in delineating a contamination plume in a landfill site: a case study in SE Brazil. J. Appl. Geophys. 55, 199–209 (2004). doi: 10.1016/j.jappgeo.2003.11.001 CrossRefGoogle Scholar
  180. Potthast, R.: Point Sources and Multipoles in Inverse Scattering Theory. Chapman & Hall/CRC, Boca Raton (2001)CrossRefzbMATHGoogle Scholar
  181. Qing, A., Lee, C.K., Jen, L.: Electromagnetic inverse scattering of two-dimensional perfectly conducting objects by real-coded genetic algorithm. IEEE Trans. Geosci. Remote Sens. 39, 665–676 (2001). doi: 10.1109/36.911123 CrossRefGoogle Scholar
  182. Qing, A.: Dynamic differential evolution strategy and applications in electromagnetic inverse scattering problems. IEEE Trans. Geosci. Remote Sens. 44, 116–125 (2006). doi: 10.1109/TGRS.2005.859347 CrossRefGoogle Scholar
  183. Qing, A., Lee, C.K.: Differential Evolution in Electromagnetics. Springer, Berlin (2010)Google Scholar
  184. Rahmat-Samii, Y., Michielssen, E.: Electromagnetic Optimization by Genetic Algorithms. J. Wiley, New York (1999)zbMATHGoogle Scholar
  185. Randazzo, A., Oliveri, G., Massa, A., Pastorino, M.: Electromagnetic inversion with the multiscaling inexact newton method-experimental validation. Microw. Opt. Technol. Lett. 53, 2834–2838 (2011). doi: 10.1002/mop.26435 CrossRefGoogle Scholar
  186. Randazzo, A.: Swarm optimization methods in microwave imaging. Int. J. Microw. Sci. Technol. 2012, 1–12 (491713) (2012). doi:  10.1155/2012/491713
  187. Randazzo, A., Estatico, C.: A regularisation scheme for electromagnetic inverse problems: application to crack detection in civil structures. Nondestruct. Test Eval. 27, 189–197 (2012). doi: 10.1080/10589759.2012.665920 CrossRefGoogle Scholar
  188. Rekanos, I.T., Kanaki, M.: Microwave imaging of two-dimensional conducting scatterers using particle swarm optimization. In: Krawczyk, A., Wiak, S., Fernandez, L.M. (eds.) Electromagnetic Fields in Mechatronics, Electrical and Electronics Engineering, pp. 84–89. IOS Press, Amsterdam (2006)Google Scholar
  189. Rekanos, I.T.: Shape reconstruction of a perfectly conducting scatterer using differential evolution and particle swarm optimization. IEEE Trans. Geosci. Remote Sens. 46, 1967–1974 (2008). doi: 10.1109/TGRS.2008.916635 CrossRefGoogle Scholar
  190. Remis, R.F., van den Berg, P.M.: On the equivalence of the Newton-Kantorovich and distorted Born methods. Inverse Probl. 16, L1–L4 (2000). doi: 10.1088/0266-5611/16/1/101 CrossRefzbMATHGoogle Scholar
  191. Robinson, J., Rahmat-Samii, Y.: Particle swarm optimization in electromagnetics. IEEE Trans. Antennas Propag. 52, 397–407 (2004). doi: 10.1109/TAP.2004.823969 MathSciNetCrossRefGoogle Scholar
  192. Roger, A.: Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem. IEEE Trans. Antennas Propag. 29, 232–238 (1981). doi: 10.1109/TAP.1981.1142588 MathSciNetCrossRefzbMATHGoogle Scholar
  193. Rubek, T., Meaney, P.M., Meincke, P., Paulsen, K.D.: Nonlinear microwave imaging for breast-cancer screening using gauss-newton’s method and the CGLS inversion algorithm. IEEE Trans. Antennas Propag. 55, 2320–2331 (2007). doi: 10.1109/TAP.2007.901993 CrossRefGoogle Scholar
  194. Sahin, A., Miller, E.L.: Object detection using high resolution near-field array processing. IEEE Trans. Geosci. Remote Sens. 39, 136–141 (2001). doi: 10.1109/36.898675 CrossRefGoogle Scholar
  195. Scapaticci, R., Catapano, I., Crocco, L.: Wavelet-based adaptive multiresolution inversion for quantitative microwave imaging of breast tissues. IEEE Trans. Antennas Propag. 60(8), 3717–3726 (2012)MathSciNetCrossRefGoogle Scholar
  196. Semnani, A., Kamyab, M., Rekanos, I.T.: Reconstruction of one-dimensional dielectric scatterers using differential evolution and particle swarm optimization. IEEE Geosci. Remote Sens. Lett. 6, 671–675 (2009). doi: 10.1109/LGRS.2009.2023246 CrossRefGoogle Scholar
  197. Semnani, A., Rekanos, I.T., Kamyab, M., Papadopoulos, T.G.: Two-dimensional microwave imaging based on hybrid scatterer representation and differential evolution. IEEE Trans. Antennas Propag. 58, 3289–3298 (2010). doi: 10.1109/TAP.2010.2055793 CrossRefGoogle Scholar
  198. Shelton, N., Warnick, K.F.: Behavior of the regularized sampling inverse scattering method at internal resonance frequencies. J. Electromagn. Waves Appl. 17, 487–488 (2003). doi: 10.1163/156939303767868991 CrossRefGoogle Scholar
  199. Slaney, M., Kak, A.C., Larsen, L.E.: Limitations of imaging with first-order diffraction tomography. IEEE Trans. Microw. Theory Tech. 32, 860–874 (1984). doi: 10.1109/TMTT.1984.1132783 CrossRefGoogle Scholar
  200. Soldovieri, F., Persico, R., Utsi, E., Utsi, V.: The application of inverse scattering techniques with ground penetrating radar to the problem of rebar location in concrete. NDT E Int. 39, 602–607 (2006). doi: 10.1016/j.ndteint.2005.12.005 CrossRefGoogle Scholar
  201. Soldovieri, F., Solimene, R.: Ground penetrating radar subsurface imaging of buried objects. Radar Technol. 105–126 (2010)Google Scholar
  202. Soldovieri, F., Lopera, O., Lambot, S.: Combination of advanced inversion techniques for an accurate target localization via GPR for demining applications. IEEE Trans. Geosci. Remote Sens. 49, 451–461 (2011a). doi: 10.1109/TGRS.2010.2051675 CrossRefGoogle Scholar
  203. Soldovieri, F., Solimene, R., Lo Monte, L., et al.: Sparse reconstruction from GPR data with applications to rebar detection. IEEE Trans. Instrum. Meas. 60, 1070–1079 (2011b). doi: 10.1109/TIM.2010.2078310 CrossRefGoogle Scholar
  204. Solimene, R., Pierri, R.: Number of degrees of freedom of the radiated field over multiple bounded domains. Opt. Lett. 32, 3113 (2007). doi: 10.1364/OL.32.003113 CrossRefGoogle Scholar
  205. Solimene, R., Soldovieri, F., Prisco, G., Pierri, R.: Three-dimensional through-wall imaging under ambiguous wall parameters. IEEE Trans. Geosci. Remote Sens. 47, 1310–1317 (2009). doi: 10.1109/TGRS.2009.2012698 CrossRefGoogle Scholar
  206. Solimene, R., Leone, G., Dell’Aversano, A.: MUSIC algorithms for rebar detection. J. Geophys. Eng. 10, 064006 (2013a). doi: 10.1088/1742-2132/10/6/064006 CrossRefGoogle Scholar
  207. Solimene, R., Maisto, M.A., Pierri, R.: Role of diversity on the singular values of linear scattering operators: the case of strip objects. J. Opt. Soc. Am. A 30, 2266 (2013b). doi: 10.1364/JOSAA.30.002266 CrossRefGoogle Scholar
  208. Solimene, R., Maisto, M.A., Romeo, G., Pierri, R.: On the singular spectrum of the radiation operator for multiple and extended observation domains. Int. J. Antennas Propag. 2013, 1–10 (2013c). doi: 10.1155/2013/585238 CrossRefGoogle Scholar
  209. Solimene, R., Catapano, I., Gennarelli, G., et al.: A unified mathematical overview of SAR imaging algorithms and some unconventional applications. IEEE Signal Process (2014a) (In print)Google Scholar
  210. Solimene, R., Cuccaro, A., Dell’Aversano, A., et al.: Ground clutter removal in GPR surveys. IEEE J. Sel. Top Appl. Earth Obs. Remote Sens. 7, 792–798 (2014a). doi: 10.1109/JSTARS.2013.2287016 CrossRefGoogle Scholar
  211. Solimene, R., D’Alterio, A., Gennarelli, G., Soldovieri, F.: Estimation of soil permittivity in presence of antenna-soil interactions. IEEE J. Sel Top. Appl. Earth Obs. Remote Sens. 7, 805–812 (2014b). doi: 10.1109/JSTARS.2013.2268576 CrossRefGoogle Scholar
  212. Solimene, R., Dell’Aversano, A.: Some remarks on time-reversal MUSIC for two-dimensional thin PEC scatterers. IEEE Geosci. Remote Sens. Lett. 11, 1163–1167 (2014). doi: 10.1109/LGRS.2013.2288516 CrossRefGoogle Scholar
  213. Soumekh, M.: Synthetic Aperture Radar Signal Processing with MATLAB Algorithms. Wiley, New York (1999)Google Scholar
  214. Stolt, R.H.: Migration by fourier transform. Geophysics 43, 23–48 (1978). doi: 10.1190/1.1440826 CrossRefGoogle Scholar
  215. Sun, C.-H., Chiu, C.-C., Li, C.-L.: Time-domain inverse scattering of a two-dimensional metallic cylinder in slab medium using asynchronous particle swarm optimization. Prog. Electromagn. Res. M 14, 85–100 (2010). doi: 10.2528/PIERM10051101 CrossRefGoogle Scholar
  216. Sun, J.: An eigenvalue method using multiple frequency data for inverse scattering problems. Inverse Probl. 28, 025012 (2012). doi: 10.1088/0266-5611/28/2/025012 CrossRefGoogle Scholar
  217. Taylor, A.E., Lay, D.C.: Introduction to Functional Analysis, 2d edn. Wiley, New York (1980)zbMATHGoogle Scholar
  218. Tikhonov, A.N., Arsenine, V.I.: Solution to Ill-posed Problems. Halsted, York (1977)Google Scholar
  219. Watters, T.R., Leuschen, C.J., Plaut, J.J., et al.: MARSIS radar sounder evidence of buried basins in the northern lowlands of Mars. Nature 444, 905–908 (2006). doi: 10.1038/nature05356 CrossRefGoogle Scholar
  220. Weile, D.S., Michielssen, E.: Genetic algorithm optimization applied to electromagnetics: a review. IEEE Trans. Antennas Propag. 45, 343–353 (1997). doi: 10.1109/8.558650 CrossRefGoogle Scholar
  221. Van den Berg, P.M., Kleinman, R.E.: A total variation enhanced modified gradient algorithm for profile reconstruction. Inverse Probl. 11, L5–L10 (1995). doi: 10.1088/0266-5611/11/3/002 CrossRefzbMATHGoogle Scholar
  222. Van den Berg, P.M., Kleinman, R.E.: A contrast source inversion method. Inverse Probl. 13, 1607–1620 (1997). doi: 10.1088/0266-5611/13/6/013 CrossRefzbMATHGoogle Scholar
  223. Van den Berg, P.M., Abubakar, A.: Contrast source inversion method: state of art. Prog. Electromagn. Res. 34, 189–218 (2001). doi: 10.2528/PIER01061103 CrossRefGoogle Scholar
  224. Van der Wielen, A., Courard, L, Nguyen, F.: Detection of thin layers into concrete with static and CMP measurements. In: Proceedings of 14th International Conference on Ground Penetrating Radar GPR, pp 530–535. IEEE, Shanghai, China (2012)Google Scholar
  225. Winters, D.W., Van Veen, B.D., Hagness, S.C.: A sparsity regularization approach to the electromagnetic inverse scattering problem. IEEE Trans. Antennas Propag. 58, 145–154 (2010). doi: 10.1109/TAP.2009.2035997 CrossRefGoogle Scholar
  226. Zhuge, X., Yarovoy, A.G., Savelyev, T., Ligthart, L.: Modified Kirchhoff migration for UWB MIMO array-based radar imaging. IEEE Trans. Geosci. Remote Sens. 48, 2692–2703 (2010). doi: 10.1109/TGRS.2010.2040747 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ilaria Catapano
    • 1
    Email author
  • Andrea Randazzo
    • 2
  • Evert Slob
    • 3
  • Raffaele Solimene
    • 4
  1. 1.Institute for Electromagnetic Sensing of the Environment—National Research Council of ItalyNaplesItaly
  2. 2.Department of Electrical, Electronic, Telecommunications Engineering, and Naval ArchitectureUniversity of GenoaGenoaItaly
  3. 3.Department of Geoscience and EngineeringDeft Univeristy of TechnologyDelftThe Netherlands
  4. 4.Department of Industrial and Information EngineeringSecond University of NaplesAversaItaly

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