Constrained Pseudoinverses for the Electromagnetic Inverse Source Problem

Inverse source strategies have proven to be quite relevant for several applications in advanced electromagnetics. These schemes are based on the solution of ill-posed problems in which current or near-field distributions are reconstructed from far-field (or from less informative field) information. Standard strategies, that can include physical constraints such as Love conditions, often rely on standard pseudoinverse definitions and yield solutions that are, at times, far from the physical ones. This work proposes a different approach focusing on defining and analyzing a new family of pseudoinverses that takes advantage of small-in-dimension subspaces containing a priori information. The new solutions returned by the new pseudoinverses will be a suitable average between a solution living entirely in the vector space containing the a priori information and a solution obtained via norm-minimizing approaches. The contribution presents both theoretical analyses and numerical experiments showing the practical effectiveness of the novel mathematical tool.