A robust iterative method for Born inversion

We present a robust iterative method to solve the inverse scattering problem in cases where the Born approximation is valid. We formulate this linearized inverse problem in terms of the unknown material contrast and the unknown contrast sources and we solve the problem by minimizing a cost functional consisting of two terms. The first term represents the differences between the actual data and the modeled data, while the second term represents the misfit in the constitutive relations between the contrast sources and the incident fields. In each iteration, the contrast sources and the contrast are reconstructed alternatingly, using subsequently a conjugate gradient step for the contrast source updates and a direct inversion of a diagonal matrix for the contrast. A further regularization with a multiplicative regularization factor is discussed. In this regularization procedure the relative variation of the contrast is minimized as well. As a test case we consider the two-dimensional (2-D) transverse magnetic polarization problem. Synthetic numerical examples are presented in order to compare the presented algorithm to the traditional Born algorithm. Results with respect to the inversion of experimental data are presented as well. In addition, some inversion results for the subsurface sensing problem, both in two and three dimensions, are presented.