Magnetic resonance-based inverse scattering has been proposed to extract tissue electrical properties (EP). We present an improved implementation of the Global Maxwell Tomography (GMT) EP mapping technique, with two new cost functions and an extension that uses piecewise linear basis functions to represent fields for higher accuracy. GMT does not make symmetry assumptions, is fully 3D, and is robust to noise. We validated the new GMT version with various numerical experiments, using a heterogeneous head model with realistic EP and a phantom with tissue-mimicking EP. We showed, for the first time, that artifact-free accurate reconstruction of EP is possible.