PIER B | |

Progress In Electromagnetics Research B | ISSN: 1937-6472 |

Home > Vol. 16 > pp. 407-432
## A PRIORI MODELING FOR GRADIENT BASED INVERSE SCATTERING ALGORITHMSBy S. Nordebo and M. Gustafsson
Abstract:
This paper presents a Fisher information based Bayesian approach to analysis and design of the regularization and preconditioning parameters used with gradient based inverse scattering algorithms. In particular, a one-dimensional inverse problem is considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A priori parameter modeling is considered with linear, exponential and arctangential parameter scalings and robust preconditioners are obtained by choosing the related scaling parameters based on a Fisher information analysis of the known background. The Bayesian approach and a principal parameter (singular value) analysis of the stochastic Cramer-Rao bound provide a natural interpretation of the regularization that is necessary to achieve stable inversion, as well as an indicator to predict the feasibility of achieving successful reconstruction in a given problem set-up. In particular, the Tikhonov regularization scheme is put into a Bayesian estimation framework. A time-domain least-squares inversion algorithm is employed which is based on a quasi-Newton algorithm together with an FDTD-electromagnetic solver. Numerical examples are included to illustrate and verify the analysis.
2. Bertero, M., "Linear inverse and ill-posed problems," 3. Bucci, O. M., L. Crocco, T. Isernia, and V. Pascazio, "Subsurface inverse scattering problems: Quantifying qualifying and achieving the available information," 4. Chew, W. C. and Y. M.Wang, "Reconstruction of twodimensional permittivity distribution using the distorted born iterative method," 5. Colton, D. and R. Kress, 6. Fhager, A., M. Gustafsson, S. Nordebo, and M. Persson, "A statistically based preconditioner for two-dimensional microwave tomography," 7. Fhager, A. and M. Persson, "Comparison of two image reconstruction algorithms for microwave tomography," 8. Fletcher, R., 9. Goharian, M., M. Soleimani, and G. Moran, "A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data," 10. Greenbaum, A., 11. Gustafsson, M., "Wave Splitting in Direct and Inverse Scattering Problems,", PhD thesis, Lund University, Department of Electromagnetic Theory, P. O. Box 118, Lund S-22100, Sweden, 2000, http://www.eit.lth.se. 12. Gustafsson, M. and S. He, "An optimization approach to twodimensional time domain electromagnetic inverse problems," 13. Gustafsson, M. and S. Nordebo, "Cramer --- Rao lower bounds for inverse scattering problems of multilayer structures," 14. Habashy, T. M. and A. Abubakar, "A general framework for constraint minimization for the inversion of electromagnetic measurements," 15. Isakov, V., 16. Kaipio, J. and E. Somersalo, 17. Kay, S. M., 18. Kelley, C. T., 19. Kirsch, A., 20. Knapp, C. H. and G. C. Carter, "The generalized correlation method for estimation of time delay," 21. Kristensson, G. and R. J. Krueger, "Direct and inverse scattering in the time domain for a dissipative wave equation. Part 1: Scattering operators," 22. Marengo, E. A. and R. W. Ziolkowski, "Nonradiating and minimum energy sources and their fields: Generalized source inversion theory and applications," 23. Nordebo, S., A. Fhager, M. Gustafsson, and M. Persson, "A systematic approach to robust preconditioning for gradient based inverse scattering algorithms," 24. Nordebo, S., M. Gustafsson, and B. Nilsson, "Fisher information analysis for two-dimensional microwave tomography," 25. Nordebo, S., M. Gustafsson, and K. Persson, "Sensitivity analysis for antenna near-field imaging," 26. Nordebo, S. and M. Gustafsson, "Statistical signal analysis for the inverse source problem of electromagnetics," 27. Pierri, R., A. Liseno, and F. Soldovieri, "Shape reconstruction from PO multifrequency scattered fields via the singular value decomposition approach," 28. Pierri, R. and F. Soldovieri, "On the information content of the radiated fields in the near zone over bounded domains," 29. Soleimani, M., C. N. Mitchell, R. Banasiak, R. Wajman, and A. Adler, "Four-dimensional electrical capacitance tomography imaging using experimental data," 30. Taflove, A. and S. C. Hagness, 31. Tarantola, A., 32. Tipping, M. E., "Sparse Bayesian learning and the relevance vector machine," 33. Van Trees, H. L., 34. Yu, Y. and L. Carin, "Three-dimensional Bayesian inversion with application to subsurface sensing," 35. Yu, Y., B. Krishnapuram, and L. Carin, "Inverse scattering with sparse Bayesian vector regression," |

© Copyright 2010 EMW Publishing. All Rights Reserved