On a Constrained Pseudoinverse for the Electromagnetic Inverse Source Problem

TL;DR

This paper introduces a generalized pseudoinverse method for electromagnetic inverse source problems, incorporating additional constraints from evanescent fields to improve solution stability and accuracy.

Contribution

It proposes a novel generalized pseudoinverse that relaxes Moore-Penrose conditions, enabling the inclusion of evanescent field constraints in inverse source reconstructions.

Findings

Enhanced stability with evanescent field constraints

Improved reconstruction accuracy in practical scenarios

Favorable performance demonstrated in case studies

Abstract

Inverse source approaches have shown their relevance for several applications in the past years. They rely on the solution of an ill-posed problem where near-field/current data is reconstructed starting from far-field (or less informative field) information. Standard strategies, including the physically constrained ones using Love conditions, result in linear systems to be pseudoinverted which are still ill-conditioned due to the lack of information from the evanescent fields. In this work we present a generalized pseudoinverse for those problems that allows the inclusion of extra constraints from the evanescent field space, when available. This is obtained by dropping some of the standard Moore-Penrose (MP) requirements and using the resulting degrees of freedom to obtain a generalized pseudoinverse that shows favorable performance in several cases of practical interest.