Regularized modified gradient method for inverse scattering problems

Electromagnetic waves are used in various inverse scattering problems such as geophysical exploration, nondestructive evaluation or medical imaging. They are concerned with determining the location and the spatial variations of some physical properties inside a test area. Several algorithms have been developed to solve this nonlinear and ill-posed problem. We consider an iterative scheme based on the modified gradient method (MGM) introduced by R.E. Kleinman and P.M. van den Berg (see J. Comput. Appl. Math., vol.42, p.17-35, 1992). It updates simultaneously the unknown field in the scattering domain and the unknown constitutive material by minimizing a cost functional. Some modifications have been done to the MGM formulation in order to take into account that the object to be reconstructed is complex. The authors investigate the possibility of two regularization schemes based on an edge-preserving approach and a Markovian energy related to the weak membrane model. Taking advantage of the proposed MGM formulation, the regularizing scheme introduces two functionals which act separately on the real and imaginary parts of the object to be estimated. To test the regularized extended MGM algorithm, some results using real data are presented.