In order to measure in vivo resistivity of tissues in the thorax, the possibility of combining anatomical data extracted from high-resolution images with multiple-electrode impedance measurements, a priori knowledge of the range of tissue resistivities, and a priori data on the instrumentation noise is assessed in this study. A statistically constrained minimum-mean-square error estimator (MIMSEE) that minimizes the effects of linearization errors and instrumentation noise is developed and compared to the conventional least-squares error estimator (LSEE). The MIMSEE requires a priori signal and noise information. The statistical constraint signal information was obtained from a priori knowledge of the physiologically allowed range of regional resistivities. The noise constraint information was obtained from a priori knowledge of the linearization error and the instrumentation noise. The torso potentials were simulated by employing a three-dimensional canine torso model. The model consists of four different conductivity regions: heart, right lung, left lung, and body. It is demonstrated that the statistically constrained MIMSEE performs significantly better than the LSEE in determining resistivities, The results based on the torso model indicate that regional resistivities can be estimated to within 40% accuracy of their true values by utilizing a statistically constrained MIMSEE, even if the instrumentation noise is comparable to the measured torso potentials. The errors obtained using the LSEE with the same linearized transfer function and level of instrumentation noise were about five times larger than those obtained using the MIMSEE. For larger measurement errors the MIMSEE performs even better when compared to the LSEE.