POCS approach for imaging dielectric objects

Historically, thè first approach to electromagnetic imaging was to linearize in some way the scattering equation in order to inveri it from thè knowledge of thè incident fieid and thè scattered field in some region outside thè object under test. The first-order (Bom or Rytov) approximations that are adopted to linearize thè problem, however, considerably limit the ability of thè reconstruction algorithms to represent thè object vvith sufficient fidelity. Indeed, thè linear algorithms are essentially Fourier-based, bui, if linearization is not strictly justified, thè measurements yield only a distorted version of thè object's Fourier transform (on a limited spatial-frequency domain). For these reasons, since thè late 70's, nonlinear reconstruction algorithms nave been developed. Exploiting thè nonlinearity of thè scattering equation allovvs us to obtain quantitative imaging, while vvith linear methods we could only expect to locate more or less exactly thè inhomogeneities in thè permittivity of thè object. Unfortunately, most of thè nonlinear algorithms developed so far are based on thè optimization of strongly nonconvex functionals, and are thus very expensive from a computational viewpoint. Another approach, besides thè totally linear and thè nonlinear ones, is to exploit a linear data model along with generic prior knowledge on thè compact support, thè reality, and thè positivity of thè contrast function for dielectric objects. This approach promises to give us much better images than thè ones obtained by using both linear data models and linear reconstruction algorithms. Moreover, thè calculations required are less expensive than thè ones required by fully nonlinear algorithms.