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Permittivity Profile Estimation Based on Non-Radiating Equivalent Source (2D Case)

By Shahed Shahir, Mehrbod Mohajer, Arash Rohani, and Safieddin Safavi-Naeini
Progress In Electromagnetics Research B, Vol. 50, 157-175, 2013


This paper presents a new approach to the electromagnetic inverse scattering formulation of the permittivity profile estimation. The proposed approach is particularly effective for the cases where unknown objects are made of a finite number of homogeneous regions. This approach prevents the need for the Born approximation initial guess and updating the internal total electric field iteratively. The solution to the inverse source problem and scattering problem is not unique. To address the non-uniqueness issue, we have defined the non-radiating objective functions. By minimizing this objective function and applying some constraints, we have been able to obtain a unique permittivity profile. The simulation results indicate that the low-contrast and high-contrast permittivity profiles are accurately estimated by the proposed method. The distinguishing feature of the proposed approach is that by including the non-radiating part of the equivalent source, the unknown permittivity profile becomes the solution to a minimization problem, which is much less computationally intensive as compared to existing methods using iterative field calculation over the entire domain, when applied to large (in terms of wavelength) objects. The high performance of the proposed method for noisy measured data has also been verified.


Shahed Shahir, Mehrbod Mohajer, Arash Rohani, and Safieddin Safavi-Naeini, "Permittivity Profile Estimation Based on Non-Radiating Equivalent Source (2D Case)," Progress In Electromagnetics Research B, Vol. 50, 157-175, 2013.


    1. Autierin, , R., , M. Durso, C. Eyraud, A. Litman, V. Pascazio, and T. Isernia, "3d inversion of fresneldatabase with 3d Markov random field," Session 3P6 Inverse Scattering Probelms: Open Problems and New Challenges, , 559, 2010.

    2. Berry, , E., , A. J. Fitzgerald, N. N. Zinov'ev, G. C. Walker, S. Homer-Vanniasinkam, C. D. Sudworth, R. E. Miles, J. M. Chamberlain, and M. A., "Optical properties of tissue measured using terahertz pulsed imaging," Proceedings of SPIE , Vol. 5030, 459-470, 2003.

    3. Bertero, , M., , T. A. Poggio, and V. Torre, "Ill-posed problems in early vision," Proceedings of the IEEE, Vol. 76, No. 8, 869-889, 1988.

    4. Bojarski, , N. N., "Inverse scattering," Technical report, DTIC Document,, 1973.

    5. Caorsi, , S., , G. Gragnani, M. Pastorino, G. Zunino, and et al, "Microwave imaging based on a Markov random ¯eld model," IEEE Transactions on Antennas and Propagation, Vol. 42, No. 3, 293-303, 1994.

    6. Chen, X., "Application of signal-subspace and optimization method in reconstructing extended scatterers," JOSA A, Vol. 26, 1022-1026, 2009.

    7. Chen, X., "Subspace-based optimization method for solving inverse scattering problems," IEEE Trans. Geosci. Remote Sens , Vol. 48, No. 1, 42-49, 2010.

    8. Chew, , W. C., Y. M. Wang, and , "Reconstruction of two-dimensional permittivity distribution using the distorted born iterative method," IEEE Transactions on Medical Imaging, Vol. 9, No. 2, 218-225, 1990.

    9. Chew, , W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, 1995.

    10. Chiappe, , M. and G. L. Gragnani, "Analytical solution to inverse electromagnetic scattering: Shape and position reconstruction of dielectric objects," IEEE International Workshop on Imaging Systems and Techniques, 1-6, 2007.

    11. Crawley, , D., , C. Longbottomm, V. P.Wallace, B. Cole, D. Arnone, and M. Pepper, "Three-dimensional terahertz pulse imaging of dental tissue," Journal of Biomedical Optics, Vol. 8, No. 2, 303-307, 2003.

    12. 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 Sens., Vol. 39, 339-346, 2001.

    13. Fieguth, P., , "Statistical Image Processing and Multidimensional Modeling," Spring, Vol. 155, , 2010.

    14. Scaf, , C. E. S. G., , J. Morais, and L. C. M. Loffredo, "A survey of radiographic measurement estimation in assessment of dental implant length," Oral Surgery, Oral Medicine, Oral Pathology, Oral, Radiology and Endodontology, Vol. 103, , No. 53, 2007.

    15. Gilmore, , C., P. Mojabi, A. Zakaria, M. Ostadrahimi, C. Kaye, S. Noghanian, L. Shafai, S. Pistorius, and J. LoVetri, "A wideband microwave tomography system with a novel frequency selection procedure," IEEE Transactions on Biomedical Engineering , Vol. 57, No. 4, 894-903, 2010.

    16. Gilmore, C., P. Mojabi, A. Zakaria, S. Pistorius, and J. LoVetri, "On super-resolution with an experimental microwave tomography system," IEEE Antennas and Wireless Propagation Letters, Vol. 9, 393-396, 2010.

    17. Gragnani, , G., "Electromagnetic imaging using closed-form radiating and non-radiating currents," Mediterranean Microwave Symposium, 1-6, 2009.

    18. Gragnani, G., "Two-dimensional nonradiating currents for imaging systems: Theoretical development and preliminary assessment," IET Microwaves, Antennas Propagation, Vol. 3, No. 8, 1164-1171, 2009.

    19. Gragnani, , G. and M. D. Mendez, "An improved electromagnetic imaging procedure using non-radiating sources," Mediterranean Microwave Symposium, 188-191, 2010.

    20. Hajihashemi, , M. R. and M. El-Shenawee, "Inverse scattering of three-dimensional PEC objects using the level-set method," Progress In Electromagnetics Research, Vol. 116, 23-47, 2011.

    21. Harrington, , R. F., Time-Harmonic Electromagnetic Fields, The IEEE Press Series, Pscataway, NJ, 2001.

    22. Johnson, , S., , Y. Tae-Hoon, and R. Jung-Woong, "Inverse scattering solutions of scalar Helmholtz wave equation by a multiple source moment method," Electron. Lett.,, Vol. 19, 130-132, 1983.

    23. Lavarello, R. J. and M. L. Oelze, "Tomographic reconstruction of three-dimensional volumes using the distorted born iterative method," IEEE Transactions on Medical Imaging, Vol. 10, No. 28, 1643-1653, 2009.

    24. Lee, , K. C., , J.-S. Ou, and M. C. Fang, "Application of SVD noise-reduction technique to PCA based radar target recognition," Progress In Electromagnetics Research, Vol. 81, 447-459, 2008.

    25. Markel, , V. A., V. Mital, and J. C. Schotland, "Inverse problem in optical diffusion tomography iii inversion formulas and singular value decomposition," J. Opt. Soc. Am. A, Vol. 20, No. 5, 890-902, 2003.

    26. Muller, , C., "Electromagnetic radiation patterns and sources," IRE Transactions on Antennas and Propagation, Vol. 4, No. 3, 224-232, 1956.

    27. Ney, , M. M., , A. M. Smith, and S. S. Stuchly, "A solution of electromagnetic imaging using pseudoinverse transformation," IEEE Transactions on Medical Imaging,, 3-4, 1984.

    28. Nguyen, , K. L., M. L. Johns, and L. F. Gladden, "Three-dimensional imaging with a terahertz quantum cascade laser," Optics Express, Vol. 14, No. 6, 2006.

    29. Porter, R. and A. Devaney, "Holography and the inverse source problem," Journal of Optical Society of America, Vol. 72, 327-330, 1982.

    30. Porter, , R. P., "Diffraction-limited, scalar image formation with holograms of arbitrary shape," Journal of the Optical Society of America,, Vol. 60, No. 8, 1051-1059, 1970.

    31. Richmond, J. H., "Scattering by a dielectric cylinder of arbitrary cross section shape," IEEE Antennas and Wireless Propagation , Vol. 13, No. 3, 334-341, 1965.

    32. Tachibana, H. and K. Matsumoto, "Applicability of x-ray computerized tomography in endodontics," Dental Traumatology, Vol. 6, No. 1, 16-20, 1990.

    33. Wang, Y. , W. Chew, and , "An iterative solution of the two-dimensional electromagnetic inverse scattering problem," International Journal of Imaging Systems and Technology, Vol. 1, No. 1, 100-108, 1989.

    34. Winters, , D. W., 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 Transactions on Antennas and Propagation, Vol. 54, 3517-3528, 2006.

    35. Winters, , D. W., B. D. Van Veen, and S. C. Hagness, "A sparsity regularization approach to the electromagnetic inverse scattering problem," IEEE Transactions on Antennas Propagation,, Vol. 58, 145-154, 2010.

    36. Wirgin, , A., "The inverse crime," ArXiv preprint mathph/0401050, 2004.

    37. Wolf, , E., "Three-dimensional structure determination of semi transparent objects from holographic data," Optical Communication, Vol. 1, No. 4, 153-156, 1969.