Dual regularization in one-dimensional inverse scattering problem

Inverse scattering problems in subsurface diagnostics of inhomogeneous media

“…However, our results of our study of more simple one-dimensional problems [7][8][9] demonstrate serious limitations of such iterative approach for large perturbations, when the Born approximation (used as the first guess of iterative method) gives considerable deviations from true solutions. To overcome these restrictions of perturbation theory, the new method of dual regularization based on the Lagrange approach in the optimization theory has been proposed and applied to solve such problems [4][5][6][7][8][9].…”

“…To overcome these restrictions of perturbation theory, the new method of dual regularization based on the Lagrange approach in the optimization theory has been proposed and applied to solve such problems [4][5][6][7][8][9]. It can be based on initial Maxwell equations, and results of this application to one-dimensional problems of low-frequency sounding of Earth crust conductivity profile and to retrieve profiles of diffuse perturbations of permittivity in multilayer structures of Xray optics, show its ability to retrieve very strong variations of sounded parameters.…”

“…In the dual regularization algorithm for 3D problems proposed here by analogy with those for onedimensional problems [7][8][9][10], it is necessary to satisfy the condition …”

“…Among them, inverse scattering problems can be also applied in various methods of electromagnetic tomography 3D distributions of media parameters [2][3][4][5] and in profile retrieval of one-dimensional inhomogeneities [6][7][8][9][10]. In frameworks of electromagnetic perturbation theory, inverse scattering problems in has been reduced to the non-linear integral equation that can be solved iteratively at each step as linear Fredholm integral equations of the 1 st kind, beginning with the Born approximation using, for example, Tikhonov's method of generalized discrepancy.…”

One-dimensional inverse scattering problem

“…Results of the numerical study [7] for low-frequency conductivity sounding have demonstrated serious limitations of such approach for large perturbations, when the Born approximation (first guess of iterative method) is inapplicable. To overcome these restrictions of perturbation theory, the new method of dual regularization based on the Lagrange approach in the optimization theory [8] has been applied in this problem to solve initial Maxwell equations [9]. Results show its ability to retrieve very strong variations of conductivity profiles.…”