Inverse source problem from the knowledge of radiated field over multiple rectilinear domains

Abstract—This paper deals with an inverse source problem starting from the knowledge of the radiated field in Fresnel and near zone. In particular, here we are concerned with a 2D geometry characterized by a rectilinear magnetic source and measurement rectilinear domains in Fresnel and near zone. The effect of the added knowledge of the radiated field over a second observation domain is investigated via the Singular Values Decomposition of the radiation operator and we point out how the addition of a second observation domain allows us always to achieve a better noise rejection. Also, we determine conditions under which the knowledge of the field over the second domain increases the information content (as the number of singular values of the radiation operator before their asymptotic decay) for both the Fresnel and near zone cases. Finally reconstruction examples with noise-free and noisy data are presented. 1