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.
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.
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.
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.
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.
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.
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.
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.
9. Deng, Y. and X. Liu, "Electromagnetic imaging methods for nondestructive evaluation applications," Sensors, Vol. 11, No. 12, 11774-11808, 2011.
10. Zoughi, R., Microwave Non-destructive Testing and Evaluation, Kluwer, The Netherlands, 2000.
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.
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.
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.
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.
15. Hagness, S. C., "Microwave imaging in medicine: Promises and future challenges," Proc. URSI Gen. Assem., 53706, 2008.
16. Semenov, S., "Microwave tomography: Review of the progress towards clinical applications," Philos. Trans. A. Math. Phys. Eng. Sci., Vol. 367, 3021-3042, 2009.
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.
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.
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.
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.
21. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, New York, 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
37. Hadamard, J., "Lectures on Cauchy's problem in linear partial differential equations," Physiology, 334, 1923.
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.
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.
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.
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.
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.