Linear and nonlinear inversion of GPR data

We discuss the linear and nonlinear inverse scattering problem. In cases where the Born approximation is valid, we obtain an inverse inverse problem, which is formulated as an optimization problem in terms of the unknown material contrast and the unknown contrast sources. The constitutive relation between these quantities acts as a regularizing constraint. A further regularization with a multiplicative regularization factor is discussed. In this regularization procedure the relative variation of the contrast is minimized as well. We illustrate the robustness of the inversion algorithm for a 2D problem, where we have all the views around the unknown object. In addition, some inversion results for the subsurface sensing problem, both in 2D and 3D, are presented. In the latter example, we show that a full nonlinear inversion scheme may improve the results.