Imaging Small PEC Spheres by a Linear $\delta$ Approach

The problem of localizing small inhomogeneities from the knowledge of their scattered field is dealt with. In particular, the case of small perfect electric conducting spheres is of concern, with the scattered field data collected under multistatic/multifrequency/single-view or multistatic/single-frequency/multiview far zone configurations. The multiple scattering between the spheres is neglected, and their locations are represented as the supports of the Dirac delta functions. This allows one to cast the problem as the inversion of a linear integral operator, with the delta functions being the unknowns of the problem. The inversion of this linear integral operator is achieved by means of the truncated singular value decomposition. The performance of the linear inversion algorithm against the model error (i.e., for situations where the multiple scattering is not negligible) is investigated by numerical simulations. Furthermore, the effect of noise is also analyzed by corrupting the data by an uncorrelated additive white Gaussian process.