Dielectric tensor tomography reconstructs the three-dimensional dielectric tensors of microscopic objects and provides information about the crystalline structure orientations and principal refractive indices. Because dielectric tensor tomography is based on transmission measurement, it suffers from the missing cone problem, which causes poor axial resolution, underestimation of the refractive index, and halo artifacts. In this study, we study the application of total variation and positive semi-definiteness regularization to three-dimensional tensor distributions. In particular, we demonstrate the reduction of artifacts when applied to dielectric tensor tomography.