A novel approach to scatterers localization problem

A new approach to find the number and locations of electromagnetic scatterers (sources) from one view, one frequency field data is presented. The case of scatterers (sources) with dimensions comparable to the wavelength is considered. First, in order to devise an effective technique, a new relevant property of the electromagnetic field, the point source spectral content, is introduced and its relationship with both the sliding windowed Fourier transform of the field and the local bandwidth function is discussed. To enlighten its usefulness it is also shown that a footprint of the scattering system encoding information on its geometry can be easily extracted from the scattered field by exploiting this new property. On this basis, the new localization technique is introduced. In order to restrict the search region, the minimum circular envelope enclosing the scatterers is found by purposely introducing a new technique exploiting the effective bandwidth of the radiated field. Then, the number and locations of scatterers is retrieved by using the field local quantitative feature previously introduced, without the complexities of the full inverse problem as it is usually done by the traditional approaches. In this way, not only a simplified technique is obtained but also the ill-posedness of the problem and the noise effects are significantly mitigated. The effectiveness of the proposed technique and its overall performance with respect to a singular value decomposition based approach are proved by means of a numerical analysis.