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Application of Differential Evolution to a Two-Dimensional Inverse Scattering Problem

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Differential Evolution in Electromagnetics

Part of the book series: Evolutionary Learning and Optimization ((ALO,volume 4))

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Introduction

Inverse scattering problems [1]-[2] are of great importance in non-destructive and non-invasive evaluation applications. Typically, the region of investigation is inaccessible and has to be evaluated using different approaches including electromagnetic waves. In such scenarios, the region is illuminated by electromagnetic waves from various directions and the electromagnetic fields scattered by objects in the region are measured at various receivers. The electrical and geometric properties of objects present inside the region are then reconstructed using the measured scattered electromagnetic fields.

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References

  1. 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)

    Article  Google Scholar 

  2. 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 

  3. 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)

    Article  Google Scholar 

  4. 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)

    Article  Google Scholar 

  5. Qing, A.: Electromagnetic imaging of two-dimensional perfectly conducting cylinders with transverse electric scattered field. IEEE Trans. Antennas Propagation 50(12), 1786–1794 (2002)

    Article  Google Scholar 

  6. Li, Y., Rao, L., He, R., Xu, G., Wu, Q., Ge, M., Yan, W.: Image reconstruction of EIT using differential evolution algorithm. In: 25th IEEE Annual Int. Conf. Engineering Medicine Biology Society, September 17-21, vol. 2, pp. 1011–1014 (2003)

    Google Scholar 

  7. 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)

    Article  MathSciNet  Google Scholar 

  8. Caorsi, S., Massa, A., Pastorino, M., Raffetto, M., Randazzo, A.: Microwave imaging of cylindrical inhomogeneities based on an analytical forward solver and multiple illuminations. In: IEEE Int. Workshop Imaging Systems Techniques, Stresa, Italy, May 14, pp. 100–105 (2004)

    Google Scholar 

  9. Chen, X., Grzegorczyk, T.M., Wu, B.I., Pacheco Jr., J., Kong, J.A.: Robust method to retrieve the constitutive effective parameters of metamaterials. Physical Review E 70(1), art. no. 016608 (July 2004)

    Google Scholar 

  10. Chen, X., O’Neill, K., Barrowes, B.E., Grzegorczyk, T.M., Kong, J.A.: Application of a spheroidal-mode approach and a differential evolution algorithm for inversion of magneto-quasistatic data in UXO discrimination. Inverse Problems 20(6), s27–s40 (2004)

    Article  Google Scholar 

  11. Li, Y., Rao, L., He, R., Xu, G., Guo, X., Yan, W., Wang, L., Yang, S.: Three EIT approaches for static imaging of head. In: Annual Int. Conf. IEEE Engineering Medicine Biology Society, San Francisco, CA, September 1-5, vol. 1, pp. 578–581 (2004)

    Google Scholar 

  12. Li, Y., Rao, L.Y., He, R.J., Xu, G.Z., Wu, Q., Yan, W.L., Dong, G.Y., Yang, Q.X.: A novel combination method of electrical impedance-tomography inverse problem for brain imaging. In: 11th IEEE Biennial Conf. Electromagnetic Field Computation, Seoul, Korea, June 6-9, pp. 1848–1851 (2004)

    Google Scholar 

  13. Massa, A., Pastorino, M., Randazzo, A.: Reconstruction of two-dimensional buried objects by a differential evolution method. Inverse Problems 20(6), S135–S150 (2004)

    Article  MathSciNet  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. Chen, X., Wu, B.I., Kong, J.A., Grzegorczyk, T.M.: Retrieval of the effective constitutive parameters of bianisotropic metamaterials. Phys. Rev. E 71(4), 46610 (2005)

    Article  Google Scholar 

  16. Shubitidze, F., O’Neill, K., Shamatava, I., Sun, K., Paulsen, K.: Analyzing multi-axis data versus scalar data for UXO discrimination. SPIE, vol. 5794, pp. 336–345 (2005)

    Google Scholar 

  17. Shubitidze, F., O’Neill, K., Shamatava, I., Sun, K., Paulsen, K.: Combined differential evolution and surface magnetic charge model algorithm for discrimination of UXO from non-UXO items: simple and general inversions. SPIE, vol. 5794, pp. 346–357 (2005)

    Google Scholar 

  18. Chen, X., Grzegorczyk, T.M., Kong, J.A.: Optimization approach to the retrieval of the constitutive parameters of slab of genral bianisotropic medium. Progress Electromagnetics Research 60, 1–18 (2006)

    Article  Google Scholar 

  19. Qing, A.: Dynamic differential evolution strategy and applications in electromagnetic inverse scattering problems. IEEE Trans. Geoscience Remote Sensing 44(1), 116–125 (2006)

    Article  Google Scholar 

  20. Agarwal, K., 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 

  21. Bachorec, T., Jirku, T., Dedkova, J.: New numerical technique for non-destructive testing of the conductive materials. In: Progress Electromagnetics Research Symp., Beijing, China, March 26-30, pp. 976–980 (2007)

    Google Scholar 

  22. Pastorino, M.: Stochastic optimization methods applied to microwave imaging: A review. IEEE Trans. Antennas Propagation 55(3), 538–548 (2007)

    Article  Google Scholar 

  23. Qing, A.: A parametric study on differential evolution based on benchmark electromagnetic inverse scattering problem. In: IEEE Congress Evolutionary Computation, Singapore, September 25-28, pp. 1904–1909 (2007)

    Google Scholar 

  24. Shubitidze, F., O’Neill, K., Barrowes, B.E., Shamatava, I., Fernandez, J.P., Sun, K., Paulsen, K.K.: Application of the normalized surface magnetic charge model to UXO discrimination in cases with overlapping signals. J. Applied Geophysics 61(3-4), 292–303 (2007)

    Article  Google Scholar 

  25. Breard, 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)

    Article  Google Scholar 

  26. Qing, A.: A study on base vector for differential evolution. In: IEEE Congress Evolutionary Computation, Hong Kong, China, June 1-6, pp. 550–556 (2008)

    Google Scholar 

  27. Rekanos, I.T.: Shape reconstruction of a perfectly conducting scatterer using differential evolution and particle swarm optimization. IEEE Trans. Geoscience Remote Sensing 46(7), 1967–1974 (2008)

    Article  Google Scholar 

  28. 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)

    Article  Google Scholar 

  29. Belkebir, K., Bonnard, S., Pezin, F., Sabouroux, P., Saillard, M.: Validation of 2D inverse scattering algorithms from multi-frequency experimental data. J. Electromagnetic Waves Applications 14(12), 1637–1667 (2000)

    Article  MATH  Google Scholar 

  30. Cheney, M.: The linear sampling method and the MUSIC algorithm. Inverse Problems 17(4), 591–595 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  31. Kirsch, A.: The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media. Inverse Problems 18(4), 1025–1040 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  32. Marklein, R., Mayer, K., Hannemann, R., Krylow, T., Balasubramanian, K., Langenberg, K.J., Schmitz, V.: Linear and nonlinear inversion algorithms applied in nondestructive evaluation. Inverse Problems 18(6), 1733–1759 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  33. Colton, D., Haddar, H., Piana, M.: The linear sampling method in inverse electromagnetic scattering theory. Inverse Problems 19(6), S105–S137 (2003)

    Article  MathSciNet  Google Scholar 

  34. Dubois, A., Belkebir, K., Saillard, M.: Localization and characterization of two-dimensional targets buried in a cluttered environment. Inverse Problems 20(6), S63–S79 (2004)

    Article  MathSciNet  Google Scholar 

  35. Kirsch, A.: The factorization method for Maxwell’s equations. Inverse Problems 20(6), S117–S134 (2004)

    Article  MathSciNet  Google Scholar 

  36. Ammari, H., Iakovleva, E., Hyeonbae, K.B.: Reconstruction of a small inclusion in a two-dimensional open waveguide. SIAM J. Applied Mathematics 65(6), 2107–2127 (2005)

    Article  MATH  Google Scholar 

  37. Cakoni, F.: Recent developments in the qualitative approach to inverse electromagnetic scattering theory. J. Computational Applied Mathematics 204(2), 242–255 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  38. Devaney, A.J.: Time reversal imaging of obscured targets from multistatic data. IEEE Trans. Antennas Propagation 53(5), 1600–1610 (2005)

    Article  MathSciNet  Google Scholar 

  39. Devaney, A.J., Marengo, E.A., Gruber, F.K.: Time-reversal-based imaging and inverse scattering of multiply scattering point targets. J. Acoustical Society America 118(5), 3129–3138 (2005)

    Article  Google Scholar 

  40. Cakoni, F., Colton, D.: Qualitative Methods in Inverse Scattering Theory: an Introduction. Springer, Berlin (2006)

    MATH  Google Scholar 

  41. Catapano, I., Crocco, L., D’Urso, M., Isernia, T.: On the effect of support estimation and of a new model in 2-D inverse scattering problems. IEEE Trans. Antennas Propagation 55(6), 1895–1899 (2007)

    Article  Google Scholar 

  42. Zhong, Y., Chen, X.: MUSIC imaging and electromagnetic inverse scattering of multiple-scattering small anisotropic spheres. IEEE Trans. Antennas Propagation 55(12), 3542–3549 (2007)

    Article  MathSciNet  Google Scholar 

  43. Agarwal, K., Chen, X.: Applicability of MUSIC-Type imaging in two-dimensional electromagnetic inverse problems. IEEE Trans. Antennas Propagation 56(10), 3217–3223 (2008)

    Article  Google Scholar 

  44. Lax, M.: Multiple scattering of waves. Reviews of Modern Physics 23, 287–310 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  45. Foldy, L.L.: The multiple scattering of waves: 1. General theory of isotropic scattering by randomly distributed scatterers. Physical Review 67, 107–119 (1945)

    Article  MATH  MathSciNet  Google Scholar 

  46. Chen, X., Agarwal, K.: MUSIC algorithm for two-dimensional inverse problems with special characteristics of cylinders. IEEE Trans. Antennas Propagation 56(6), 1808–1812 (2008)

    Article  MathSciNet  Google Scholar 

  47. Catapano, I., Crocco, L.: An imaging method for concealed targets. IEEE Trans. Geoscience Remote Sensing 47(5), 1301–1309 (2009)

    Article  Google Scholar 

  48. Chen, X., Zhong, Y.: A robust noniterative method for obtaining scattering strengths of multiply scattering point targets. J. Acoustical Society America 122(3), 1325–1327 (2007)

    Article  Google Scholar 

  49. Chiu, C.C., Chen, W.T.: Electromagnetic imaging for an imperfectly conducting cylinder by the genetic algorithm. IEEE Trans. Microwave Theory Techniques 48(11), 1901–1905 (2000)

    Article  Google Scholar 

  50. Qing, A.: Microwave imaging of parallel perfectly conducting cylinders with transverse electric scattering data. J. Electromagnetic Waves Applications 15(5), 665–685 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  51. Peterson, A.F., Ray, S.L., Mittra, R.: Computational Methods for Electromagnetics. IEEE Press, New York (1998)

    Google Scholar 

  52. Colton, D.L., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, 2nd edn. Springer, New York (1998)

    MATH  Google Scholar 

  53. Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: a Practical Approach to Global Optimization. Springer, Berlin (2005)

    Google Scholar 

  54. Qing, A.: Differential Evolution: Fundamentals and Applications in Electrical Engineering. John Wiley, New York (2009)

    Google Scholar 

  55. Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)

    MATH  Google Scholar 

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Agarwal, K., Chen, X., Zhong, Y. (2010). Application of Differential Evolution to a Two-Dimensional Inverse Scattering Problem. In: Qing, A., Lee, C.K. (eds) Differential Evolution in Electromagnetics. Evolutionary Learning and Optimization, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12869-1_4

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  • DOI: https://doi.org/10.1007/978-3-642-12869-1_4

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