The diagonalized contrast source inversion method for acoustic and electromagnetic inverse scattering problems

In the present work, we introduce a new three-step procedure which introduces a localized approximation of the scattering operator without enforcing an explicit form. The linear inversion steps follow what is referred to as the source-type integral equation (STIE) approach, in which the contrast sources are inverted for in the first step from the linear data equation. Once the contrast sources have been determined, the total internal fields follow from a direct application of the object equation. In the third and final step, the contrast function is estimated using one of two approaches. In the first approach the contrast function is estimated directly from the constitutive relation. Whereas in the second approach the contrast function is estimated by solving the data equation again, this time in terms of the contrast profile. What makes such approaches feasible, is the introduction of a diagonalization approximation of the full contrast operator. This allows the STIE approach with its three linear steps to be implemented in a robust manner, in which the nonuniqueness encountered in the reconstruction of the contrast sources in the first step is alleviated by the imposition of the diagonal form constraint on the contrast operator