Several data acquisition schemes for diffusion MRI have been proposed and explored to date for the reconstruction of the 2nd order tensor. Our main contributions in this paper are: (i) the definition of a new class of sampling schemes based on repeated measurements in every sampling point; (ii) two novel schemes belonging to this class; and (iii) a new reconstruction framework for the second scheme. We also present an evaluation, based on Monte Carlo computer simulations, of the performances of these schemes relative to known optimal sampling schemes for both 2nd and 4th order tensors. The results demonstrate that tensor estimation by the proposed sampling schemes and estimation framework is more accurate and robust.