454 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 14, NO. 3, MARCH 2017 A Simple and Effective Inverse Source Reconstruction With Minimum A Priori Information on the Source Adriana Brancaccio, Member, IEEE, and Marco Donald Migliore, Member, IEEE Abstract— A simple and effective two-step method to detect and localize scattering objects from the measurements of the total electric field, collected at a single frequency on a planar domain, is presented. The first step consists in solving a linear inverse source problem, looking for surface equivalent currents on a plane located between the measurement surface and the objects themselves. Thus, the equivalent currents associated with both the scatterer presence and the background contribution are obtained. In the second step, the support of the equivalent currents associated with the objects is separated from the background by exploiting the low-rank property of the background field. The proposed method does not require information on the source, except for its frequency, and it is easily implementable and entails a low computational burden. Experimental results validate the method. Index Terms— Electromagnetic scattering inverse problems, microwave imaging, sparse matrices. I. I NTRODUCTION T HE aim of this letter is to introduce a simple and effective two-step method to detect and localize objects from the measurements of the electric field, collected on a planar surface placed at some distances from them, in the presence of an external source providing the incident field. As is well known, one of the main difficulties in inverse scattering problems is to evaluate the “scattered” field, that is defined as the difference between the total field (quantity that is actually measured in practice) and the field in the absence of the scattering objects, that is the so-called “background” field [1]. The latter can be measured easily in laboratory conditions by removing the scatterers, but not in the case of realistic in situ measurement configurations [2]. In principle, the incident field can be simulated numerically. However, this would require detailed information about the illuminating source and the background geometry and parameters (for instance, terrain permittivity in the case of buried scatterers). The proposed method overcomes this problem by a two- step procedure. In the first step, the total measured field is related to the field radiated by equivalent surface currents Manuscript received July 26, 2016; revised September 23, 2016, November 13, 2016, and December 15, 2016; accepted December 24, 2016. Date of publication January 24, 2017; date of current version February 23, 2017. This work was supported by the European Union’s Seventh Framework Program for research, technological development, and demonstration under Grant 284996. A. Brancaccio is with DIII, Second University of Napoli, 81031 Aversa, Italy (e-mail: adriana.brancaccio@unina2.it). M. D. Migliore is with DIEI, University of Cassino and Southern Lazio, 03043 Cassino, Italy (e-mail: mdmiglio@unicas.it). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2017.2649938 located on an “investigation” plane close to the scatterers. The support of such equivalent currents is assumed as the unknown of the inverse problem. It is useful to note that the reconstruction of the equivalent currents has been discussed in a previous paper [3], but with reference to far-field mea- surements. Its extension to near-field data was presented at a conference [4] with reference to scattered field data. Its application to total field data is discussed for the first time in this letter. Usually, direct and inverse electromagnetic problems approaches using equivalent currents refer to volumetric cur- rents in the case of dielectric objects [5] and to surface currents in the case of metallic objects [6]–[8]. In both the cases, the current in the volume or on the surface of the object is considered. Our approach is significantly different. We consider 2-D equivalent currents for any kind of object (dielectric or metallic and 3-D). Furthermore, the equivalent current is evaluated on a surface that is different from the object surface. These characteristics allow to greatly reduce the computational burden of the algorithm. The aim of the second step is to distinguish the equiva- lent currents associated with the scattering objects from the ones related to the background contribution. To this end, the algorithm exploits the low-rank properties of the background field and the sparse properties of the field scattered by the objects [9]. The latter property holds for localized small scatterers. This procedure was briefly discussed in [10] and included among the examples of applications of the minimum trace norm regularization technique, but it was never experi- mentally tested earlier. In brief, the proposed algorithm requires a linear inversion for the first step, while the second step can be performed using efficient convex minimization programs [11]. Thus, from a numerical point of view, the method proves to be both fast and easy to program into MATLAB, and it is easy to implement in that it does not require information on the source. In addition, the sparse representation of the scattered field characteristic makes it applicable to fields such as demining, as shown in [10]. II. SCATTERING MODEL We assume that objects (either metallic or dielectric) are at some distances from the measurement plane and illuminated by an external source. The tangent component of the field is measured over a finite domain  of the measurement plane. In the following, we suppose that the objects stand in free space, according to the experimental configuration used in Sections IV and V. Consequently, the background field is the incident field radiated by the source. However, the proposed approach also works in the case of objects buried 1545-598X © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.