A nonlinear effective inversion algorithm based on the Arnoldi solution of the forward scattering problem

Usually, the forward scattering problem is solved iteratively, using, for example, the conjugate gradient (CG) method. Hence, every time there is a change in the constitutive parameter, one is forced to perform a full run of the CG algorithm. We propose a method, which avoids this procedure. By exploiting the structure of the forward scattering operator we can construct an approximate solution of the forward scattering problem, in which the constant contrast-function appears as a parameter. The Arnoldi algorithm is the cornerstone of our method. With the help of this algorithm we construct a so-called Arnoldi decomposition of the forward scattering operator. Using the shift-invariance property of this decomposition we can compute solutions for many contrasts at once by inverting a small scaled matrix of coefficients only.