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In this paper, we consider a two-dimensional inverse medium problem from noisy observation data. We propose effective reconstruction algorithms to detect the number, the location and the size of the piecewise constant medium within a body, and then we try to recover the unknown shape of inhomogeneous media. This problem is nonlinear and ill-posed, thus we should consider stable and elegant approaches in order to improve the corresponding approximation. We give several examples to show the viability...
We deal with an inverse scattering problem whose aim is to determine the thickness variation of a dielectric thin coating located on a conducting structure of unknown shape. The inverse scattering problem is solved through the application of the Generalized Impedance Boundary Conditions (GIBCs) which contain the thickness, curvature as well as material properties of the coating and they have been obtained in the previous work [B. Aslanyürek, H. Haddar and H.Şahintürk, Wave Motion 48 (2011) 681–700]...
The numerical solution of ill-posed problems requires suitable
regularization techniques. One possible option is to consider time
integration methods to solve the Showalter differential equation
numerically. The stopping time of the numerical integrator corresponds
to the regularization parameter. A number of well-known
regularization methods such as the Landweber iteration or the
Levenberg-Marquardt method can be interpreted as variants of the
Euler method for solving the Showalter differential...
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