We investigate the noise sensitivity in various Diffusion Tensor MRI acquisition protocols in sixteen human ex vivo hearts. In particular, we compare the accuracy of protocols with various numbers of excitations and diffusion sensitizing directions for estimating the principal diffusion directions in the myocardium. It is observed that noise sensitivity decreases as the number of excitations and the number of sensitizing directions increase (and hence as the acquisition time increases). To reduce the effects of noise and to improve the results obtained with a smaller number of excitations and/or a smaller number of sensitizing directions, we introduce a 3-D edge-preserving regularization method operating on diffusion weighted images. It allows to maintain the quality of the principal diffusion direction field while minimizing the acquisition time, which is a necessary step for in vivo diffusion tensor MR imaging of the human heart.