Geophysical data are frequently collected with a fine sample interval along traverse lines but with a coarser sampling in the direction perpendicular to the traverses. This disparity in sampling intervals is particularly evident when magnetic data are collected simultaneously with airborne electromagnetic data. Interpolating this traverse data onto an evenly spaced 2D grid can result in aliasing artifacts. For example, narrow linear structures that trend at acute angles to the traverse lines are imaged as a thick/thin/thick feature, looking like a boudinage or string of beads. Applying the anisotropic diffusion process to the resulting grids of data removes the artifacts, but the grid values close to the traverses are altered significantly from their initial values. The altered values are therefore not faithful to the original traverse data. The anisotropic diffusion algorithm can be modified to constrain values close to the original traverses. This modification removes the aliasing artifacts and produces a data grid faithful to the original traverse data. Some small artifacts along the traverse lines in the final data grid become more evident when grids containing derivative data (such as the analytic signal) are generated from the new data grid. However, these small traverse-line artifacts can be removed with standard microleveling procedures. The constrained anisotropic diffusion process is iterative, and some experimentation is required to determine the appropriate number of iterations.