1. Butler, C., "General analysis of a narrow slot in a conducting screen between half-spaces of different electromagnetic properties," Radio Sci., Vol. 22, No. 7, 1149-1154, 1987.
doi:10.1029/RS022i007p01149 Google Scholar
2. Bleistein, N. and J. K. Cohen, "Nonuniqueness in inverse source problems in acoustics and electromagnetics," Journal of Mathematical Physics, Vol. 18, No. 2, 194-201, February 1977.
doi:10.1063/1.523256 Google Scholar
3. Devaney, A. J., "Nonuniqueness in the inverse scattering problem," Journal of Mathematical Physics, Vol. 19, No. 7, 1526-31, July 1978.
doi:10.1063/1.523860 Google Scholar
4. Devaney, V. and E. Wolf, "Radiating and nonradiating classical currents distributions and the fields they generate," Physical Review D , Vol. 8, No. 4, 1044-47, August 1973.
doi:10.1103/PhysRevD.8.1044 Google Scholar
5. Porter, R. P. and A. J. Devaney, "Holography and the inverse source problem," J. Opt. Soc. Am., Vol. 72, 327-330, 1982.
doi:10.1364/JOSA.72.000327 Google Scholar
6. Stone, R., "review and examination of results on uniqueness in inverse problems," Radio Science, Vol. 22, No. 6, 1026-1030, November 1987.
doi:10.1029/RS022i006p01026 Google Scholar
7. Parker, R. L., "Understanding inverse theory," Ann. Rev. Earth Planet. Sci., Vol. 5, 35-64, 1977.
doi:10.1146/annurev.ea.05.050177.000343 Google Scholar
8. Backus, G. E. and J. F. Gilbert, "Numerical application of a formalism for geophysical inverse problems," Geopgys. J. Astron. Soc., Vol. 13, 247-276, 1967.
doi:10.1111/j.1365-246X.1967.tb02159.x Google Scholar
9. Backus, G. and F. Gilbert, "The resolving power of gross Earth data," Geopgys. J. Astron. Soc., Vol. 16, 169-205, 1968.
doi:10.1111/j.1365-246X.1968.tb00216.x Google Scholar
10. Backus, G. and F. Gilbert, "Uniqueness in the inversion of inaccurate gross Earth data," Phil. Trans. R. Soc. London. Ser. A, Vol. 266, 123-192, March 1970.
doi:10.1098/rsta.1970.0005 Google Scholar
11. Habashy, T. M., E. Y. Chow, and D. G. Dudley, "Profile inversion using the renormalized source-type integral equation approach," IEEE Transactions on Antenna and Propagation, Vol. 38, 668-682, 1990.
doi:10.1109/8.53495 Google Scholar
12. Habashy, T. M., R. W. Groom, and B. R. Spies, "Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering," Journal of Geophysical Research, Vol. 98, No. B2, 1759-1775, February 1993.
doi:10.1029/92JB02324 Google Scholar
13. Born, M. and E. Wolf, Principles of Optics, Pergamon, New York, 1980.
14. Rytov, S. M., "Diffraction of light by ultrasonic waves," Izv. Akad. Nauk. SSSR., Ser. Fiz. 2, 223, 1937. Google Scholar
15. Oristaglio, M. L., "Accuracy of the Born and Rytov approximations for the reflection and refraction at a plane interface," Optical Society of America, Vol. 2, No. 11, 1987-1992, November 1985.
doi:10.1364/JOSAA.2.001987 Google Scholar
16. Rabiner, L. R. and R. W. Schafer, Digital Processing of Speech Signals, Prentice-Hall, Englewood Cliffs, N.J., 1978.
17. Keller, J. B., "Accuracy and validity of the Born and Rytov approximations," J. Opt. Soc. Am., Vol. 59, 1003-1004, August 1969.
doi:10.1364/JOSA.59.001003 Google Scholar
18. Sancer, M. and A. D. Varvatsis, "A comparison of the Born and Rytov methods," Proceedings of the IEEE, 140-141, January 1970.
doi:10.1109/PROC.1970.7551 Google Scholar
19. Torres-Verdin, C. and T. M. Habashy, "Rapid 2.5-dimensional forward modeling and inversion via a new nonlinear sacttering approximation," Radio Science, Vol. 29, No. 4, 1051-1079, July-August 1994.
doi:10.1029/94RS00974 Google Scholar
20. Trantanella, C. J., "Beyond the Born approximation in one- and two-dimensional profile reconstruction,", Ph.D. dissertation submitted to the faculty of the Department of Electrical and Computer Engineering, University of Arizona, May 1994. Google Scholar
21. Adopley, J. A. K., "A comparison among localized approximations in one-dimensional profile reconstruction,", Ph.D. dissertation submitted to the faculty of the Department of Electrical and Computer Engineering, University of Arizona, December 1996. Google Scholar
22. Trantanella, C. J., D. G. Dudley, and K. A. Nabulsi, "Beyond the Born approximation in one-dimensional profile reconstruction," J. Opt. Soc. Am., Vol. 12, No. 7, 1469-1478, July 1995.
doi:10.1364/JOSAA.12.001469 Google Scholar
23. Ramo, S., J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, 2nd Ed., John Wiley & Sons Inc., 1984.
24. Tabbara, W., "Reconstruction of Permittivity profiles from a Spectral Analysis of the reflection Coefficient," IEEE Transactions on Antenna and Propagation, Vol. AP-27, No. 2, 241-244, March 1979.
doi:10.1109/TAP.1979.1142070 Google Scholar
25. Chipman, J. S., "On least squares with insufficient observation," Americam Statistical Association Journal, 1078-1111, December 1964.
doi:10.1080/01621459.1964.10480751 Google Scholar
26. Zhou, Y. and C. K. Rushforth, "Least-squares reconstruction of spatially limited objects using smoothness and non-negativity constraints," Applied Optics, Vol. 21, No. 7, 1249-1252, April 1982.
doi:10.1364/AO.21.001249 Google Scholar
27. Tijhuis, A. G. and C. Van Der Worm, "Iterative approach to the frequency-domain solution of the inverse-scattering problem for an inhomogeneous lossless dielectic slab," IEEE Transactions on Antenna and Propagation, Vol. AP-32, No. 7, 711-716, July 1984.
doi:10.1109/TAP.1984.1143410 Google Scholar
28. Kennett, B. L. N. and P. R. Williamson, "Subspace methods for large-scale nonlinear inversion," Mathematical Geophysics, 139-154, 1988.
doi:10.1007/978-94-009-2857-2_7 Google Scholar
29. Kennett, B. L. N., M. S. Sambridge, and P. R. Williamson, "Subspace methods for large inverse problems with multiple parameter classes," Geophysicical Journal, Vol. 94, 237-247, 1988.
doi:10.1111/j.1365-246X.1988.tb05898.x Google Scholar
30. Sambridge, M. S., "Non-linear arrival time inversion: constrained velocity anomalies by seeking smooth model in 3-D," Geophys. J. Int., Vol. 102, 653-677, 1990.
doi:10.1111/j.1365-246X.1990.tb04588.x Google Scholar
31. Oldenburg, D. W. and R. G. Eliss, "Inversion of geophysical data using an approximate inverse mapping," Geophys. J. Int., Vol. 105, 325-353, 1991.
doi:10.1111/j.1365-246X.1991.tb06717.x Google Scholar
32. Oldenburg, D. W., P. R. McGillivary, and R. G. Eliss, "Generalized subspace methodes for large-scale inverse problems," Geophys. J. Int., Vol. 114, 12-20, 1993.
doi:10.1111/j.1365-246X.1993.tb01462.x Google Scholar
33. Kleinman, R. E. and P. M. van den Berg, "An extended range-modified gradient technique for profile inversion," Radio Science, Vol. 28, No. 5, 877-884, 1993.
doi:10.1029/93RS01076 Google Scholar
34. Levenberg, K., "A method for the solution of certain non-linear problems in least squares," Quart. Appl. Math., No. 2, 164-168, July-August 1944.
doi:10.1090/qam/10666 Google Scholar
35. Marquardt, D. W., "Least squares analysis of electron paramahnetic resonance Spectra," Journal of Molecular Spectroscopy, Vol. 7, 269-279, 1961.
doi:10.1016/0022-2852(61)90360-5 Google Scholar
36. Marquardt, D. W., "Generalized inverses, ridge regression, biased linear estimation and nonlinear estimation," Tecnometrics, Vol. 2, No. 3, 591-612, 1970.
doi:10.2307/1267205 Google Scholar
37. Tikhonov, A. N. and V. Y. Arsenin, Solutions of Ill-Posed Problems, V. H. Winston & Sons, Washington, D.C., 1977.
38. Constable, S. C., R. L. Parker, and C. G. Constable, "Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data," Geophysics, Vol. 52, No. 3, 289-300, March 1987.
doi:10.1190/1.1442303 Google Scholar
39. Smith, J. T. and J. R. Booker, "Magnetotelluric inversion for minimum structure," Geophysics, Vol. 53, No. 12, 1565-1576, December 1988.
doi:10.1190/1.1442438 Google Scholar
40. Rudin, L. I., S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithm," Physica D, Vol. 60, 259-268, 1992.
doi:10.1016/0167-2789(92)90242-F Google Scholar
41. Osher, S. and L. I. Rudin, "Feature-oriented image enhancement using shock filters," SIAM J. Numer. Anal., Vol. 27, No. 4, 919-940, August 1990.
doi:10.1137/0727053 Google Scholar
42. van den Berg, P. M. and R. E. Kleinman, "A total variation enhanced modified gradient algorithm for profile reconstruction," University of Delaware Tecnical Report, Newark DE 19716, Vol. 95-4, 1995. Google Scholar
43. Oldenburg, D., "Inversion of electromagnetic data: An overview of new techniques," Surveys in Geophysics, Vol. 11, 231-270, 1990.
doi:10.1007/BF01901661 Google Scholar
44. Habashy, T. M and R. Mittra, "On some inversion methods in electromagnetics," Journal of Electromagnetic Waves and Applications, Vol. 1, No. 1, 25-58, 1987.
doi:10.1163/156939387X00081 Google Scholar
45. Miller, E. L. and A. S. Willsky, "A multiscale, statistically based inversion scheme for linearized inverse scattering problems," IEEE Transactions on Geoscience and Remote Sensing, Vol. 34, No. 2, 346-357, March 1996.
doi:10.1109/36.485112 Google Scholar
46. Zhdanov, M. S. and S. Fang, Three-dimensional quasi-linear electromagnetic inversion, Vol. 31, No. 4, 741-754, Radio Science, July-August 1996.
47. Dudley, D. G., Mathematical Foundations for Electromagnetic Theory, IEEE Press, Piscataway, NJ, USA, 1994.
doi:10.1109/9780470545232
48. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computating, 2nd Ed., Cambridge University Press, 1992.
49. Jeffreys, H., "An alternative to the rejection of observations," Proceedings of the Royal Society of London, ser. A, Vol. CXXXVII, 78-87, September 1932. Google Scholar
50. Bender, C. M. and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, Inc., 1978.