The Use of Differential Evolution for the Solution of Electromagnetic Inverse Scattering Problems

  • A. Donelli
  • A. Massa
  • G. Oliveri
  • M. Pastorino
  • A. Randazzo
Part of the Evolutionary Learning and Optimization book series (ALO, volume 4)


Inspection of penetrable objects by using differential evolution together with a recently proposed iterative multiscaling approach is discussed in this Chapter. Several new results are included concerning the reconstruction of inhomogeneous targets under various imaging conditions.


Differential Evolution Dielectric Cylinder Antenna Propagation Investigation Domain Stochastic Optimization Method 
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.


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  1. 1.
    Bertero, M., Boccacci, P.: Introduction to Inverse Problems in Imaging. IOP Press, Bristol (1998)zbMATHCrossRefGoogle Scholar
  2. 2.
    Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory. Springer, Berlin (1998)zbMATHGoogle Scholar
  3. 3.
    Qing, A., Lee, C.K., Jen, L.: Electromagnetic inverse scattering of two-dimensional perfectly conducting objects by real-coded genetic algorithm. IEEE Trans. Geoscience Remote Sensing 39(3), 665–676 (2001)CrossRefGoogle Scholar
  4. 4.
    Qing, A., Gan, Y.B.: Electromagnetic inverse problems. In: Chang, K. (ed.) Encyclopedia of RF and Microwave Engineering, vol. 2, pp. 1200–1216. John Wiley, New York (2005)Google Scholar
  5. 5.
    Harada, H., Wall, D.J.N., Takenaka, T., Tanaka, M.: Conjugate gradient method applied to inverse scattering problem. IEEE Trans. Antennas Propagation 43(8), 784–792 (1995)CrossRefGoogle Scholar
  6. 6.
    van den Berg, P.M., Kleinman, R.E.: A contrast source inversion method. Inverse Problems 13(6), 1607–1620 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Franchois, A., Joisel, A., Pichot, C., Bolomey, J.C.: Quantitative microwave imaging with a 2.45-GHz planar microwave camera. IEEE Trans. Medical Imaging 17(4), 550–561 (1998)CrossRefGoogle Scholar
  8. 8.
    Nie, Z., Feng, Y., Zhao, Y., Zhang, Y.: Variational Born iteration method and its applications to hybrid inversion. IEEE Trans. Geoscience Remote Sensing 38(4), 1709–1715 (2000)CrossRefGoogle Scholar
  9. 9.
    Tsihrintzis, G.A., Devaney, J.A.: Higher order (nonlinear) diffraction tomography: Inversion of the Rytov series. IEEE Trans. Information Theory 46(5), 1748–1751 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Zoughi, R.: Microwave Nondestructive Testing and Evaluation, Amsterdam. Kluwer Academic, The Netherlands (2000)Google Scholar
  11. 11.
    El-Shenawee, M., Rappaport, C., Miller, E.L., Silevitch, M.B.: Three-dimensional subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: Use of the steepest descent fast multipole method. IEEE Trans. Geoscience Remote Sensing 39(6), 1174–1182 (2001)CrossRefGoogle Scholar
  12. 12.
    Qing, A., Lee, C.K., Jen, L.: Electromagnetic inverse scattering of two-dimensional perfectly conducting objects by real-coded genetic algorithm. IEEE Trans. Geoscience Remote Sensing 39(3), 665–676 (2001)CrossRefGoogle Scholar
  13. 13.
    Tijhuis, G., Belkebir, K., Litman, A.C.S., de Hon, B.P.: Theoretical and computational aspects of 2-D inverse profiling. IEEE Trans. Geoscience Remote Sensing 39(6), 1316–1330 (2001)CrossRefGoogle Scholar
  14. 14.
    Abubakar, A., van den Berg, P.M., Mallorqui, J.J.: Imaging of biomedical data using a multiplicative regularized contrast source inversion method. IEEE Trans. Microwave Theory Techniques 50(7), 1761–1771 (2002)CrossRefGoogle Scholar
  15. 15.
    Bond, E.J., Li, X., Hagness, S.C., Van Veen, B.D.: Microwave imaging via space-time beamforming for early detection of breast cancer. IEEE Trans. Antennas Propagation 51(8), 1690–1705 (2003)CrossRefGoogle Scholar
  16. 16.
    Cui, T.J., Aydiner, A.A., Chew, W.C., Wright, D.L., Smith, D.V.: Three-dimensional imaging of buried objects in very lossy earth by inversion of VETEM data. IEEE Trans. Geoscience Remote Sensing 41(10), 2197–2210 (2003)CrossRefGoogle Scholar
  17. 17.
    Fang, Q., Meaney, P.M., Geimer, S.D., Streltsov, A.V., Paulsen, K.D.: Microwave image reconstruction from 3-D fields coupled to 2-D parameter estimation. IEEE Trans. Medical Imaging 23(4), 475–484 (2004)CrossRefGoogle Scholar
  18. 18.
    Zhang, Z.Q., Liu, Q.H.: Three-dimensional nonlinear image reconstruction for microwave biomedical imaging. IEEE Trans. Biomedical Engineering 51(3), 544–548 (2004)CrossRefGoogle Scholar
  19. 19.
    Belkebir, K., Saillard, M.: Testing inversion algorithms against experimental data: Inhomogeneous targets. Inverse Problems 21(6), S1–S4 (2005)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Abubakar, A., Habashy, T.M.: Nonlinear inversion of multi-frequency microwave Fresnel data using the multiplicative regularized contrast source inversion. Progress Electromagnetics Research 62, 193–201 (2006)CrossRefGoogle Scholar
  21. 21.
    Solimene, R., Soldovieri, F., Prisco, G., Pierri, R.: Three-dimensional microwave tomography by a 2-D slice-based reconstruction algorithm. IEEE Geoscience Remote Sensing Letters 4(4), 556–560 (2007)CrossRefGoogle Scholar
  22. 22.
    Arunachalam, K., Udpa, L., Udpa, S.S.: A computational investigation of microwave breast imaging using deformable reflector. IEEE Trans. Biomedical Engineering 55(2), 554–562 (2008)CrossRefGoogle Scholar
  23. 23.
    Pastorino, M.: Stochastic optimization methods applied to microwave imaging: A review. IEEE Trans. Antennas Propagation 55(3), 538–548 (2007)CrossRefGoogle Scholar
  24. 24.
    Storn, R., Price, K.V.: Differential Evolution - A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces, Technical Report TR-95-012, International Computer Science Insitute (March 1995)Google Scholar
  25. 25.
    Storn, R., Price, K.V.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optimization 11(4), 341–359 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: a Practical Approach to Global Optimization. Springer, Berlin (2005)zbMATHGoogle Scholar
  27. 27.
    Chakraborty, U.K. (ed.): Advances in Differential Evolution. Springer, Berlin (2008)zbMATHGoogle Scholar
  28. 28.
    Qing, A.: Differential Evolution: Fundamentals and Applications in Electrical Engineering. John Wiley & IEEE, New York (2009)Google Scholar
  29. 29.
    Michalski, K.A.: Electromagnetic imaging of circular-cylindrical conductors and tunnels using a differential evolution algorithm. Microwave Optical Technology Letters 27(5), 330–334 (2000)CrossRefGoogle Scholar
  30. 30.
    Michalski, K.A.: Electromagnetic imaging of elliptical-cylindrical conductors and tunnels using a differential evolution algorithm. Microwave Optical Technology Letters 28(3), 164–169 (2001)CrossRefGoogle Scholar
  31. 31.
    Qing, A.: Electromagnetic inverse scattering of multiple two-dimensional perfectly conducting objects by the differential evolution strategy. IEEE Trans. Antennas Propagation 51(6), 1251–1262 (2003)CrossRefMathSciNetGoogle Scholar
  32. 32.
    Massa, A., Pastorino, M., Randazzo, A.: Reconstruction of two-dimensional buried objects by a differential evolution method. Inverse Problems 20(6), S135–S150 (2004)CrossRefMathSciNetGoogle Scholar
  33. 33.
    Qing, A.: Electromagnetic inverse scattering of multiple perfectly conducting cylinders by differential evolution strategy with individuals in groups (GDES). IEEE Trans. Antennas Propagation 52(5), 1223–1229 (2004)CrossRefGoogle Scholar
  34. 34.
    Qing, A.: Dynamic differential evolution strategy and applications in electromagnetic inverse scattering problems. IEEE Trans. Geoscience Remote Sensing 44(1), 116–125 (2006)CrossRefGoogle Scholar
  35. 35.
    Krishna, A., Chen, X.: Application of differential evolution in 2-dimensional electromagnetic inverse problems. In: 2007 IEEE Congress Evolutionary Computation, Singapore, September 25-28, pp. 4305–4312 (2007)Google Scholar
  36. 36.
    Qing, A.: A parametric study on differential evolution based on benchmark electromagnetic inverse scattering problem. In: 2007 IEEE Congress Evolutionary Computation, Singapore, September 25-28, pp. 1904–1909 (2007)Google Scholar
  37. 37.
    Bréard, A., Perrusson, G., Lesselier, D.: Hybrid differential evolution and retrieval of buried spheres in subsoil. IEEE Geoscience Remote Sensing Letters 5(4), 788–792 (2008)CrossRefGoogle Scholar
  38. 38.
    Semnani, A., Kamyab, M.: Comparison of differential evolution and particle swarm optimization in one-dimensional reconstruction problems. In: 2008 Asia-Pacific Microwave Conf., Macau, China, December 16-20 (2008)Google Scholar
  39. 39.
    Semnani, A., Kamyab, M., Rekanos, I.T.: Reconstruction of one-dimensional dielectric scatterers using differential evolution and particle swarm optimization. IEEE Geoscience Remote Sensing Letters 6(4), 671–675 (2009)CrossRefGoogle Scholar
  40. 40.
    Caorsi, S., Donelli, M., Franceschini, D., Massa, A.: An iterative multiresolution approach for microwave imaging applications. Microwave Optical Technology Letters 32(5), 352–356 (2002)CrossRefGoogle Scholar
  41. 41.
    Franceschini, D., Donelli, M., Rocca, P., Benedetti, M., Massa, A., Pastorino, M.: Morphological processing of electromagnetic scattering data for enhancing the reconstruction accuracy of the iterative multi-scaling approach. Progress Electromagnetics Research 82, 299–318 (2008)CrossRefGoogle Scholar
  42. 42.
    Franceschini, G., Donelli, M., Azaro, R., Massa, A.: Inversion of phaseless total field data using a two-step strategy based on the iterative multiscaling approach. IEEE Trans. Geoscience Remote Sensing 44(12), 3527–3539 (2009)CrossRefGoogle Scholar
  43. 43.
    Chew, W.C.: Waves and Fields in Inhomogeneous Media. IEEE Press, New York (1995)Google Scholar
  44. 44.
    Tai, C.T.: Dyadic Green’s Functions in Electromagnetic Theory. Int. Textbook, Scranton (1971)Google Scholar
  45. 45.
    Caorsi, S., Gragnani, G.L., Pastorino, M.: A numerical approach to microwave imaging. In: 18th European Microwave Conf., Stockholm, Sweden, September 12-16, pp. 897–902 (1988)Google Scholar
  46. 46.
    Hagmann, M., Gandhi, P., Durney, C.: Upper bound cell size for moment-method solution. IEEE Trans. Microwave Theory Techniques 25(10), 831–832 (1977)CrossRefGoogle Scholar
  47. 47.
    Richmond, J.H.: Scattering by a dielectric cylinder of arbitrary cross section shape. IEEE Trans. Antennas Propagation 13(3), 334–341 (1965)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • A. Donelli
    • 1
  • A. Massa
    • 1
  • G. Oliveri
    • 1
  • M. Pastorino
    • 2
  • A. Randazzo
    • 2
  1. 1.Department of Information Engineering and Computer ScienceUniversity of TrentoItaly
  2. 2.Department of Biophysical and Electronic EngineeringUniversity of GenoaItaly

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