Usual inverse-scattering methods for the reconstruction of dielectric objects are limited by the information that can be collected at the measurement locations. In this paper, an inverse-scattering method is proposed that allows one to reconstruct the unmeasured components of the equivalent current density and then to improve the dielectric reconstruction. The mathematical formulation is provided, and the theory is supported by the results of numerical simulations. ¿ 1999 American Geophysical Union