In magnetic resonance electrical impedance tomography, among several conductivity image reconstruction algorithms, the harmonic B_z algorithm has been successfully applied to B_z data from phantoms and animals. The algorithm is, however, sensitive to measurement noise in B_z data. Especially, in in vivo animal and human experiments where injection current amplitudes are limited within a few milliampere at most, measured B_z data tend to have a low SNR. In addition, magnetic resonance (MR) signal void in outer layers of bones and gas-filled organs, for example, produces salt-pepper noise in the MR phase and, consequently, B_z images. The B_z images typically present areas of sloped transitions, which can be assimilated to ramps. Conductivity contrasts change ramp slopes in B_z images and it is critical to preserve positions of those ramps to correctly recover edges in conductivity images. In this paper, we propose a ramp-preserving denoising method utilizing a structure tensor. Using an eigenvalue analysis, we identified local regions of salt-pepper noise. Outside the identified local regions, we applied an anisotropic smoothing to reduce noise while preserving their ramp structures. Inside the local regions of salt-pepper noise, we used an isotropic smoothing. After validating the proposed denoising method through numerical simulations, we applied it to in vivo animal imaging experiments. Both numerical simulation and experimental results show significant improvements in the quality of reconstructed conductivity images.