AbstractInverse scattering algorithms forHzpolarized waves are scarce, due to the added difficulties of polarization charges. Nevertheless, the polarization charges cannot be ignored for 3D problems as well as for 2DHzproblems. This work aims to reconstruct arbitrary inhomogeneous dielectric objects fromHzscattering data using a new formulation that abandons the standard integral equation model for aT‐matrix model. This new algorithm, called local shape‐function (LSF) imaging, is modified for dielectric objects withHzincident fields, where previously the LSF algorithm was applied to metallic objects withEzincident fields. The advantage of the LSF algorithm is a more accurate modeling of the induced interfacial polarization charges. For comparison, theHzdistorted Born iterative method using integral equations is shown to be valid only for small contrasts, while the LSF algorithm converges for much larger dielectric contrasts.©1994 John Wiley&Son