Electromagnetic inverse scattering problems are compu- tation intensive, ill-posed and highly non-linear. When the scatterer lies in an inaccessible domain, the ill-posedness is even more severe as only aspect limited data is available. Typical algorithms employed for solving this inverse scattering problem involve a large scale non-linear optimization that generates values for all pixels in the investigation domain including those that might not contain any useful information about the ob ject. This communication is concerned with the local- ization in the investigation domain prior to inverse profiling of buried 2-D dielectric pipelines having circular cross section. A custom defined degree of symmetry is computed for each transmitter position, which is a measure of the symmetry of the measured (synthetic) scattered field vector. The degree of symmetry vector computed for a scat- terer is found to exhibit unique features for the geometric and electric properties of the dielectric pipeline. A probabilistic neural network is trained with the degree of symmetry vectors computed for different ob ject configurations. It classifies the test degree of symmetry vec- tor of the unknown scatterer presented to it into one of the classes that indicate the localized region in the investigation domain in which the pipeline is located. The Distorted Born Iterative procedure is em- ployed for imaging the pipeline that has been localized. The reduction in the investigation domain reduces the degrees of freedom of the in- verse scattering problem and the results are found to be much superior to those when the entire investigation domain is employed.
1. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, New York, 1995.
2. Witten, A. J., J. E. Molyneux, and J. E. Nyquist, "Ground penetrating radar tomography: Algorithm and case studies," IEEE Trans. Geosci. Remote Sensing, Vol. 32, 461-467, 1994. doi:10.1109/36.295060
3. Deming, R. and A. J. Devaney, "Diffraction tomography for multi- monostatic ground penetrating radar imaging," Inv. Problems, Vol. 13, 29-45, 1997. doi:10.1088/0266-5611/13/1/004
4. Souriau, L., B. Duchene, D. Lesselier, and R. Kleinman, "Modified gradient approach to inverse scattering of binary ob jects in stratified media," Inv. Problems, Vol. 12, 463-481, 1996. doi:10.1088/0266-5611/12/4/009
5. Lambert, M., D. Lesselier, and B. J. Kooij, "The retrieval of a buried cylindrical obstacle by a constrained modified gradient method in the H-polarization case and for Maxwellian materials," Inv. Problems, Vol. 14, 1265-1283, 1998. doi:10.1088/0266-5611/14/5/011
6. Chaturvedi, P. and R. G. Plumb, "Electromagnetic imaging of underground targets using constrained optimization," IEEE Trans. Geosci. Remote Sensing, Vol. 33, No. 5, 551-561, 1995. doi:10.1109/36.387572
7. Cui, T. J., W. C. Chew, A. A. Aydiner, and S. Chen, "Inverse scattering of two dimensional dielectric ob jects buried in lossy earth using the distorted Born iterative method," IEEE Trans. Geosci. Remote Sensing, Vol. 39, No. 2, 339-345, 2001. doi:10.1109/36.905242
8. Cui, T. J., Y. Qin, G. L. Wang, and W. C. Chew, "Low-frequency detection of two dimensional buried ob jects using high order extended Born approximations," Inv. Problems, Vol. 20, 41, 2004. doi:10.1088/0266-5611/20/6/S04
9. Thomas, V., C. Gopakumar, A. V. Praveen Kumar, V. Ham- sakutty, A. Lonappan, G. Bindu, and K. T. Mathew, "A novel technique for reducing the imaging domain in microwave imaging of two dimensional circularly symmetric scatterers," Microwave and Optical Technology Letters, Vol. 44, No. 5, 423-427, 2005. doi:10.1002/mop.20655
10. Caorsi, S. and P. Gamba, "Electromagnetic detection of dielectric cylinders by a neural network approach," IEEE Trans. Geosci. Remote Sensing, Vol. 37, No. 3, 820-827, 1999. doi:10.1109/36.752198
11. Bermani, E., S. Caorsi, and M. Rafetto, "A microwave ob ject recognition approach based on neural networks," IEEE Instru- mentation and Measurement Technology Conference Proceedings, No. 5, 1582-1585, 1999.
12. Wasserman, P. D., Advanced Methods in Neural Computing, Van Nostrand Reinhold, New York, 1993.
13. Harrington, F. R., Field Computation by Moment Methods, Macmillan, New York, 1968.
14. Duchene, B. and W. Tabbara, "Characterization of a buried cylindrical ob ject from its scattered field," IEEE Trans. Sonics Ultrasonics, Vol. 31658-663, 31658-663, 1984.
15. Specht, D. F., "Probabilistic neural networks for classification, mapping or associative memory," Proceedings of the IEEE International Conference on Neural Networks, Vol. 1, 525-532, 1988. doi:10.1109/ICNN.1988.23887