volume | PIER Journals

Abstract

Microwave inverse scattering approaches have shown their effectiveness in imaging inaccessible regions. Unfortunately, the problem at hand is strongly non-linear and ill-posed and therefore it is often solved by seeking for the global minimum of a proper functional. Nevertheless, it is also necessary to introduce suitable regularizations in order to improve the convergence of the reconstruction process toward a reliable solution. In this context, the paper presents a method that exploits an energetic constraint to define a regularization term of the cost functional. A numerical validation with single and multiple inhomogeneous lossless targets demonstrates that an improvement of the reconstruction accuracy is achievable without introducing significant computational complexity to the inverse scattering problem.

1. Bolomey, J. C., Frontiers in Industrial Process Tomography, Engineering Foundation, New York, 1995.

2. Benedetti, M., M. Donelli, and A. Massa, "Multicrack detection in two-dimensional structures by means of GA-based strategies," IEEE Trans. Antennas Propagat., Vol. 55, 205-215, Jan. 2007.
doi:10.1109/TAP.2006.888399 Google Scholar

3. Kharkovsky, S. and R. Zoughi, "Microwave and millimeter wave nondestructive testing and evaluation --- Overview and recent advances," IEEE Instrum. and Meas. Mag., Vol. 10, 26-38, Apr. 2007.
doi:10.1109/MIM.2007.364985 Google Scholar

4. Meaney, P. M, M. W. Fanning, L. Dun, S. P. Poplack, and K. D. Paulsen, "A clinical prototype for active microwave imaging of the breast ," IEEE Trans. Microwave Theory Tech., Vol. 48, 1841-1853, Nov. 2000. Google Scholar

5. O'Halloran, M., R. Conceicao, D. Byrne, M. Glavin, and E. Jones, "FDTD modeling of the breast: A review," Progress In Electromagnetics Research B, Vol. 18, 1-24, 2009.
doi:10.2528/PIERB09080505 Google Scholar

6. Lazaro, A., D. Girbau, and R. Villarino, "Simulated and experimental investigation of microwave imaging using UWB," Progress In Electromagnetic Research, Vol. 94, 263-280, 2009.
doi:10.2528/PIER09061004 Google Scholar

7. Cui, T. J., W. C. Chew, A. A. Aydiner, and S. Chen, "Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method," IEEE Trans. Geosci. Remote Sensing, Vol. 39, 339-346, Feb. 2001.
doi:10.1109/36.905242 Google Scholar

8. Bermani, E., A. Boni, S. Caorsi, and A. Massa, "An innovative real-time technique for buried object detection," IEEE Trans. Geosci. Remote Sensing, Vol. 41, 927-931, 2003.
doi:10.1109/TGRS.2003.810928 Google Scholar

9. Crocco, L., M. D'Urso, and T. Isernia, "The contrast source-extended Born model for 2D subsurface scattering problems," Progress In Electromagnetics Research B, Vol. 17, 343-359, 2009.
doi:10.2528/PIERB09080502 Google Scholar

10. Catapano, I., L. Crocco, R. Persico, M. Pieraccini, and F. Soldovieri, "Linear and nonlinear microwave tomography approaches for subsurface prospecting: Validation on real data," IEEE Antennas Wireless Propag. Lett., Vol. 5, 49-53, Dec. 2006.
doi:10.1109/LAWP.2006.870363 Google Scholar

11. Zhang, Z. Q. and Q. H. Liu, "Applications of the BiCGS-FFT method to 3-D induction well logging problems," IEEE Geosci. Remote Sensing, Vol. 41, 856-869, May 2003. Google Scholar

12. Caorsi, S., A. Massa, M. Pastorino, and M. Donelli, "Improved microwave imaging procedure for nondestructive evaluations of two-dimensional structures," IEEE Trans. Antennas Propagat., Vol. 52, 1386-1397, 2004.
doi:10.1109/TAP.2004.830254 Google Scholar

13. Yu, Y., T. Yu, and L. Carin, "Three-dimensional inverse scattering of a dielectric target embedded in a lossy half-space," IEEE Trans. Geosci. Remote Sensing, Vol. 42, 957-973, May 2004.
doi:10.1109/TGRS.2003.820601 Google Scholar

14. Li, F., Q. H. Liu, and L.-P. Song, "Three dimensional reconstruction of objects buried in layered media using Born and distorted Born iterative methods," IEEE Trans. Geosci. Remote Sensing, Vol. 1, 107-111, Apr. 2004.
doi:10.1109/LGRS.2004.826562 Google Scholar

15. Franceschini, G., A. Abubakar, T. M. Habashy, and A. Massa, "A comparative assessment among iterative linear solvers dealing with electromagnetic integral equations in 3D inhomogeneous anisotropic media," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 7, 899-914, 2007.
doi:10.1163/156939307780749048 Google Scholar

16. Colton, D. and R. Krees, Inverse Acoustics and Electromagnetic Scattering Theory, Springer-Verlag, Berlin, Germany, 1992.

17. Bucci, O. M. and T. Isernia, "Electromagnetic inverse scattering: Retrievable information and measurement strategies," Radio. Sci., Vol. 32, 2123-2138, Dec. 1997.
doi:10.1029/97RS01826 Google Scholar

18. Bucci, O. M., L. Crocco, T. Isernia, and V. Pascazio, "Subsurface inverse scattering problems: Quantifying, qualifying and achieving the available information ," IEEE Trans. Geosci. Remote Sensing, Vol. 39, 2527-2537, Nov. 2001. Google Scholar

19. Litman, A., "Reconstruction by level sets of N-ary scattering obstacles ," Inv. Probl., Vol. 21, S131-S152, Dec. 2005.
doi:10.1088/0266-5611/21/6/S10 Google Scholar

20. Dorn, O. and D. Lesselier, "Level set methods for inverse scattering," Inv. Probl., Vol. 22, R67-R131, Aug. 2006.
doi:10.1088/0266-5611/22/4/R01 Google Scholar

21. Aramini, R., M. Brignone, and M. Piana, "The linear sampling method without sampling," Inv. Probl., Vol. 22, 2237-2254, Dec. 2006.
doi:10.1088/0266-5611/22/6/020 Google Scholar

22. Rekanos, I. T., "Shape reconstruction of a perfectly conducting scatterer using di®erential evolution and particle swarm optimization," IEEE Trans. Geosci. Remote Sensing, Vol. 46, 1967-1974, 1974.
doi:10.1109/TGRS.2008.916635 Google Scholar

23. Kleinman , R. E. and P. M. van den Berg, "A modified gradient method for two-dimensional problems in tomography," J. Comput. Appl. Math., Vol. 42, 17-35, 1992.
doi:10.1016/0377-0427(92)90160-Y Google Scholar

24. Van den Berg, P. M. and A. Abubakar, "Contrast source inversion method: State of the art," Progress In Electromagnetics Research, Vol. 34, 189-218, 2001.
doi:10.2528/PIER01061103 Google Scholar

25. Rocca, P., M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, "Evolutionary optimization as applied to inverse scattering problems," Inv. Probl., Vol. 25, No. 12, Article No. 123003, Dec. 2009. Google Scholar

26. Garnero, L., A. Franchois, J.-P. Hugonin, C. Pichot, and N. Joachimowicz, "Microwave imaging-complex permittivity reconstruction by simulated annealing," IEEE Trans. Microwave Theory Tech., Vol. 39, 1801-1807, Nov. 1991. Google Scholar

27. Caorsi, S., A. Massa, and M. Pastorino, "A computational technique based on a real-coded genetic algorithm for microwave imaging purposes," IEEE Trans. Geosci. Remote Sensing, Vol. 38, 1697-1708, Jul. 2000. Google Scholar

28. Caorsi, S., A. Massa, M. Pastorino, and A. Randazzo, "Electromagnetic detection of dielectric scatterers using phaseless synthetic and real data and the memetic algorithm," EEE Trans. Geosci. Remote Sensing, Vol. 41, 2745-2753, 2003.
doi:10.1109/TGRS.2003.815676 Google Scholar

29. Caorsi, S., M. Donelli, A. Lommi, and A. Massa, "Location and imaging of two-dimensional scatterers by using a particle swarm algorithm ," Journal of Electromagnetic Waves and Applications, Vol. 18, 481-494, 2004.
doi:10.1163/156939304774113089 Google Scholar

30. Donelli, M. and A. Massa, "Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers," IEEE Trans. Microwave Theory Tech., Vol. 53, 1761-1776, May 2005.
doi:10.1109/TMTT.2005.847068 Google Scholar

31. Donelli, M., G. Franceschini, A. Martini, A. Massa, and , "An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems," IEEE Trans. Geosci. Remote Sensing, Vol. 44, 298-312, 2006.
doi:10.1109/TGRS.2005.861412 Google Scholar

32. Huang, T. and A. S. Mohan, "A microparticle swarm optimizer for the reconstruction of microwave images," IEEE Trans. Antennas Propagat., Vol. 55, 568-576, Mar. 2007.
doi:10.1109/TAP.2007.891545 Google Scholar

33. Crocco, L. and T. Isernia, "Inverse scattering with real data: Detecting and imaging homogeneous dielectric objects," Inv. Probl., Vol. 17, 1573-1583, Dec. 2001.
doi:10.1088/0266-5611/17/6/302 Google Scholar

34. Abubakar, A., P. M. van den Berg, and S. Y. Semenov, "Two- and three-dimensional algorithms for microwave imaging and inverse scattering," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 2, 209-231, Feb. 2003.
doi:10.1163/156939303322235798 Google Scholar

35. Jones, D. S., The Theory of Electromagnetism, Pergamon Press, Oxford, U.K., 1964.

36. Franceschetti, G., Elctromagnetics: Theory, Techniques, and Engineering Paradigms, Plenum Press, New York, London, 1997.

37. Richmond, J. H., "Scattering by a dielectric cylinder of arbitrary cross section shape," IEEE Trans. Antennas Propagat., Vol. 13, 334-341, May 1965.
doi:10.1109/TAP.1965.1138427 Google Scholar

38. Burden, R. L. and J. D. Faires, Numerical Analysis, Brooks-Cole, Pacific Grove, CA, 2001.

Dr. Davide Franceschini