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Simultaneous nonlinear reconstruction of two‐dimensional permittivity and conductivity
Author(s) -
Habashy Tarek M.,
Oristaglio Michael L.,
Hoop Adrianus T.
Publication year - 1994
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/93rs03448
Subject(s) - basis function , permittivity , nonlinear system , mathematical analysis , inversion (geology) , scattering , mathematics , basis (linear algebra) , minification , norm (philosophy) , iterative method , algorithm , physics , optics , mathematical optimization , geometry , dielectric , geology , paleontology , optoelectronics , quantum mechanics , structural basin , political science , law
A new inversion algorithm for the simultaneous reconstruction of permittivity and conductivity recasts the nonlinear inversion as the solution of a coupled set of linear equations. The algorithm is iterative and proceeds through the minimization of two cost functions. At the initial step the data are matched through the reconstruction of the radiating or minimum norm scattering currents; subsequent steps refine the nonradiating scattering currents and the material properties inside the scatterer. Two types of basis functions are constructed for the nonradiating currents: “invisible” (global) basis functions, which are appropriate for discrete measurements and nonradiating (local) basis functions, which are useful in studying the limit of continuous measurements. Reconstructions of square cylinders from multiple source receiver measurements at a single frequency show that the method can handle large contrasts in material properties.