volume | PIER Journals

Abstract

A regularization is integrated with Forward-Backward Time-Stepping (FBTS) method which is formulated in time-domain utilizing Finite-Difference Time-Domain (FDTD) method to solve the nonlinear and ill-posed problem arisen in the microwave inverse scattering problem. FBTS method based on a Polak-Ribiète-Polyak conjugate gradient method is easily trapped in the local minima. Thus, we extend our work with the integration of edge-preserving regularization technique due to its ability to smooth and preserve the edges containing important information for reconstructing the dielectric profiles of the targeted object. In this paper, we propose a deterministic relaxation with Mean Square Error algorithm known as DrMSE in FBTS and integrate it with the automated edge-preserving regularization technique. Numerical simulations are carried out and prove that the reconstructed results are more accurate by calculating the edge-preserving parameter automatically.

1. Pastorino, M., Microwave Imaging, 1st Ed., John Wiley, 2010.
doi:10.1002/9780470602492

2. Kim, Y. J., L. Jofre, F. De Flaviis, and M. Q. Feng, "Microwave reflection tomographic array for damage detection of civil structures," IEEE Trans. Antennas Propag., Vol. 51, No. 11, 3022-3032, 2003.
doi:10.1109/TAP.2003.818786 Google Scholar

3. Benedetti, M., M. Donelli, A. Martini, M. Pastorino, A. Rosani, and A. Massa, "An innovative microwave-imaging technique for nondestructive evaluation: Applications to civil structures monitoring and biological bodies inspection," IEEE Trans. Instrum. Meas., Vol. 55, 1878-1884, 2006.
doi:10.1109/TIM.2006.884287 Google Scholar

4. Langenberg, K. J., K. Mayer, and R. Marklein, "Nondestructive testing of concrete with electromagnetic and elastic waves: Modeling and imaging," Cem. Concr. Compos., Vol. 28, No. 4, 370-383, 2006.
doi:10.1016/j.cemconcomp.2006.02.010 Google Scholar

5. Randazzo, A. and C. Estatico, "A regularisation scheme for electromagnetic inverse problems: Application to crack detection in civil structures," Nondestruct. Test. Eval., Vol. 27, No. 3, 189-197, 2012.
doi:10.1080/10589759.2012.665920 Google Scholar

6. Qaddoumi, N., R. Zoughi, and G. W. Carriveau, "Microwave detection and depth determination of disbonds in low-permittivity and low-loss thick sandwich composites," Res. Nondestruct. Eval., Vol. 8, No. 1, 51-63, 1996.
doi:10.1080/09349849609409587 Google Scholar

7. Kharkovsky, S. and R. Zoughi, "Microwave and millimeter wave nondestructive testing and evaluation - Overview and recent advances," IEEE Instrum. Meas. Mag., Vol. 10, No. 2, 26-38, 2007.
doi:10.1109/MIM.2007.364985 Google Scholar

8. Zoughi, R. and S. Kharkovsky, "Microwave and millimetre wave sensors for crack detection," Fatigue Fract. Eng. Mater. Struct., Vol. 31, No. 8, 695-713, 2008.
doi:10.1111/j.1460-2695.2008.01255.x Google Scholar

9. Deng, Y. and X. Liu, "Electromagnetic imaging methods for nondestructive evaluation applications," Sensors, Vol. 11, No. 12, 11774-11808, 2011.
doi:10.3390/s111211774 Google Scholar

10. Zoughi, R., Microwave Non-destructive Testing and Evaluation, Kluwer, 2000.
doi:10.1007/978-94-015-1303-6

11. Pastorino, M., "Recent inversion procedures for microwave imaging in biomedical, subsurface detection and nondestructive evaluation applications," Measurement: Journal of the International Measurement Confederation, Vol. 36, No. 3-4, 257-269, 2004.
doi:10.1016/j.measurement.2004.09.006 Google Scholar

12. Pastorino, M. and A. Randazzo, "Buried object detection by an inexact newton method applied to nonlinear inverse scattering," Int. J. Microw. Sci. Technol., Vol. 2012, 2012. Google Scholar

13. Estatico, C., A. Fedeli, M. Pastorino, and A. Randazzo, "Buried object detection by means of a Lp Banach-space inversion procedure," Radio Sci., Vol. 50, No. 1, 41-51, Jan. 2015.
doi:10.1002/2014RS005542 Google Scholar

14. Rufus, E. and Z. C. Alex, "Microwave imaging system for the detection of buried objects using UWB antenna - An experimental study," PIERS Proceedings, 786-788, Kuala Lumpur, Malaysia, Mar. 27-30, 2012. Google Scholar

15. Hagness, S. C., "Microwave imaging in medicine: Promises and future challenges," Proc. URSI Gen. Assem., 53706, 2008. Google Scholar

16. Semenov, S., "Microwave tomography: Review of the progress towards clinical applications," Philos. Trans. A. Math. Phys. Eng. Sci., Vol. 367, 3021-3042, 2009.
doi:10.1098/rsta.2009.0092 Google Scholar

17. Meaney, P. M., K. D. Paulsen, and D. College, "Challenges on microwave imaging supported by clinical results," Proc. Int. Work. Biol. Eff. Electromagn. Fields, 10-14, 2010. Google Scholar

18. Hassan, M. and A. M. El-Shenawee, "Review of electromagnetic techniques for breast cancer detection," IEEE Rev. Biomed. Eng., Vol. 4, 103-118, 2011.
doi:10.1109/RBME.2011.2169780 Google Scholar

19. Wei, N. S., K. A. H. Ping, L. S. Yee, W. A. B. W. Zainal Abidin, T. Moriyama, and T. Takenaka, "Reconstruction of extremely dense breast composition utilizing inverse scattering technique integrated with frequency-hopping approach," ARPN J. Eng. Appl. Sci., Vol. 10, No. 18, 8479-8484, 2015. Google Scholar

20. Salvad, A., M. Pastorino, R. Monleone, A. Randazzo, T. Bartesaghi, G. Bozza, and S. Poretti, "Microwave imaging of foreign bodies inside wood trunks," IST 2008 - IEEE Workshop on Imaging Systems and Techniques Proceedings, 88-93, 2008.
doi:10.1109/IST.2008.4659947 Google Scholar

21. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, 2012.

22. Massa, A., D. Franceschini, G. Franceschini, M. Pastorino, M. Raffetto, and M. Donelli, "Parallel GA-based approach for microwave imaging applications," IEEE Trans. Antennas Propag., Vol. 53, No. 10, 3118-3127, 2005.
doi:10.1109/TAP.2005.856311 Google Scholar

23. Donelli, M. and A. Massa, "A computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers," IEEE Trans. Microw. Theory Tech., Vol. 53, No. 5, 1761-1776, 2005.
doi:10.1109/TMTT.2005.847068 Google Scholar

24. Rekanos, I. T., "Time-domain inverse scattering using Lagrange multipliers: An iterative FDTD-based optimization technique," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 2, 271-289, 2003.
doi:10.1163/156939303322235824 Google Scholar

25. Winters, D. W., E. J. Bond, B. D. Van Veen, and S. C. Hagness, "Estimation of the frequency-dependent average dielectric properties of breast tissue using a time-domain inverse scattering technique," IEEE Trans. Antennas Propagat., Vol. 54, No. 11, 3517-3528, 2006.
doi:10.1109/TAP.2006.884296 Google Scholar

26. Takenaka, T., H. Jia, and T. Tanaka, "Microwave imaging of electrical property distributions by a forward-backward time-stepping method," Journal of Electromagnetic Waves and Applications, Vol. 14, No. 12, 1609-1626, 2000.
doi:10.1163/156939300X00383 Google Scholar

27. Takenaka, T., T. Tanaka, H. Harada, and S. He, "FDTD approach to time-domain inverse scattering problem for stratified lossy media," Microw. Opt. Technol. Lett., Vol. 16, No. 5, 292-296, 1997.
doi:10.1002/(SICI)1098-2760(19971205)16:5<292::AID-MOP8>3.0.CO;2-A Google Scholar

28. Ping, K. A. H., T. Moriyama, T. Takenaka, and T. Tanaka, "Two-dimensional forward-backward time-Stepping approach for tumor detection in dispersive breast tissues," 2009 Mediterranean Microw. Symp. (MMS), 1-4, 2009. Google Scholar

29. Blanc-Feraud, L., P. Charbonnier, G. Aubert, and M. Barlaud, "Nonlinear image processing: Modeling and fast algorithm for regularization with edge detection," Proc. IEEE-ICIP, 474-477, 1995. Google Scholar

30. Lobel, P., C. Picbota, L. Blanc Feraud, and M. Barlaud, "Conjugate gradient algorithm with edge-preserving regularization for image reconstruction from experimental data," IEEE Antennas Propag. Soc. Int. Symp. 1996, AP-S. Dig., Vol. 1, 644-647, 1996.
doi:10.1109/APS.1996.549680 Google Scholar

31. Chew Chie, A. S., K. A. Hong Ping, Y. Guang, N. S. Wei, and N. Rajaee, "Preliminary results of integrating Tikhonov's regularization in Forward-Backward Time-Stepping technique for object detection," Appl. Mech. Mater., Vol. 833, 170-175, Apr. 2016.
doi:10.4028/www.scientific.net/AMM.833.170 Google Scholar

32. Kaltenbacher, B., A. Kirchner, and B. Vexler, "Adaptive discretizations for the choice of a Tikhonov regularization parameter in nonlinear inverse problems," Inverse Probl., Vol. 27, No. 12, 125008, Dec. 2011.
doi:10.1088/0266-5611/27/12/125008 Google Scholar

33. Qin, Y. M. and I. R. Ciric, "Dielectric body reconstruction with current modelling and Tikhonov regularisation," Electron. Lett., Vol. 29, No. 16, 1427, 1993.
doi:10.1049/el:19930956 Google Scholar

34. Calvetti, D., S. Morigi, L. Reichel, and F. Sgallari, "Tikhonov regularization and the L-curve for large discrete ill-posed problems," J. Comput. Appl. Math., Vol. 123, 423-446, 2000.
doi:10.1016/S0377-0427(00)00414-3 Google Scholar

35. Charbonnier, P., L. Blanc-Féraud, G. Aubert, and M. Barlaud, "Deterministic edge-preserving regularization in computed imaging," IEEE Trans. Image Process., Vol. 6, No. 2, 298-311, 1997.
doi:10.1109/83.551699 Google Scholar

36. Yong, G., K. A. H. Ping, A. S. C. Chie, S. W. Ng, and T. Masri, "Preliminary study of Forward-Backward Time-Stepping technique with edge-preserving regularization for object detection applications," 2015 International Conference on BioSignal Analysis, Processing and Systems (ICBAPS), 77-81, 2015.
doi:10.1109/ICBAPS.2015.7292222 Google Scholar

37. Hadamard, J., "Lectures on Cauchy's problem in linear partial differential equations," Physiology, 334, 1923. Google Scholar

38. Hebert, T. and R. Leahy, "A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors," IEEE Trans. Med. Imaging, 194-202, 1989.
doi:10.1109/42.24868 Google Scholar

39. Green, P. J., "Bayesian reconstructions from emission tomography data using a modified EM algorithm," IEEE Trans. Med. Imaging, Vol. 9, No. 1, 84-93, Mar. 1990.
doi:10.1109/42.52985 Google Scholar

40. Geman, S. and D. E. M. Clure, "Bayesian image analysis: An application to single photon emission tomography," Proc. Stat. Comput. Sect., 12-18, 1985. Google Scholar

41. Aubert, G., M. Barlaud, L. Blanc-Feraud, and P. Charbonnier, "A deterministic algorithm for edge-preserving computed imaging using Legendre transform," Proceedings of the 12th IAPR International Conference on Pattern Recognition (Cat. No. 94CH3440-5), 188-191, 1994.
doi:10.1109/ICPR.1994.577154 Google Scholar

42. Charbonnier, P., L. Blanc-Feraud, G. Aubert, and M. Barlaud, "Two deterministic half-quadratic regularization algorithms for computed imaging," Proceedings of 1st International Conference on Image Processing, Vol. 2, 168-172, 1994. Google Scholar

Dr. Guang Yong

Dr. Kismet Anak Hong Ping

Ms. Shafrida Sahrani

Dr. Mohamad Hamiruce Marhaban

Dr. Mohd Iqbal Sariphn

Dr. Toshifumi Moriyama

Prof. Takashi Takenaka