A modified gradient method for two-dimensional problems in tomography (Q1195373)

A method for reconstruction of a bounded two-dimensional inhomogeneous object from a measured scattered field is presented. The governing domain integral equation is solved iteratively by a successive overrelaxation technique. Convergence of this process is established for indices of refraction much larger than required for convergence of the Born approximation. Numerical results are presented for a number of representative two-dimensional objects.