THE RETRIEVAL OF A BURIED CYLINDRICAL OBSTACLE BY A CONSTRAINED MODIFIED GRADIENT-METHOD IN THE H-POLARIZATION CASE AND FOR MAXWELLIAN MATERIALS

The retrieval of an unknown, possibly inhomogeneous, penetrable cylind rical obstacle buried entirely in a known homogeneous half-space-the c onstitutive material parameters of the obstacle and of its embedding o bey a Maxwell model-is considered from single- or multiple-frequency a spect-limited data collected by ideal sensors located in air above the embedding half-space, when a small number of time-harmonic transverse electric (TE)-polarized line sources-the magnetic field H is directed along the axis of the cylinder-is also placed in air. The wavefield i s modelled from a rigorous H-field domain integral-differential formul ation which involves the dot product of the gradients of the single co mponent of H and of the Green function of the stratified environment t imes a scalar-valued contrast function which contains the obstacle par ameters (the frequency-independent, position-dependent relative permit tivity and conductivity). A modified gradient method is developed in o rder to reconstruct the maps of such parameters within a prescribed se arch domain from the iterative minimization of a cost functional which incorporates both the error in reproducing the data and the error on the field built inside this domain. Non-physical values are excluded a nd convergence reached by incorporating in the solution algorithm, fro m a proper choice of unknowns, the condition that the relative permitt ivity be larger than or equal to 1, and the conductivity be non-negati ve. The efficiency of the constrained method is illustrated from noise less and noisy synthetic data acquired independently. The importance o f the choice of the initial values of the sought quantities, the need for a periodic refreshment of the constitutive parameters to avoid the algorithm providing inconsistent results, and the interest of a frequ ency-hopping strategy to obtain finer and finer features of the obstac le when the frequency is raised, are underlined. It is also shown that though either the permittivity map or the conductivity map can be obt ained for a fair variety of cases, retrieving both of them may be diff icult unless further information is made available.