Gradient-based, singular value optimization in near-field measurements

We deal with the problem of extracting the maximum amount of information on an aperture field E_a from field measurements on a domain D_I, with a priori information on the aperture field itself. Since collecting the information on D_I is performed by means of field probes occupying different spatial positions, the problem at hand requires determining, as a function of the properties of the employed probes, of the shape and size of D_I and of the a priori information on E_a, the overall number of acquisition points and their "optimal" spatial distribution to reconstruct "at the best" the aperture field.