  It is highly desirable to know how uncertain a model's predictions are,
especially for models that are complex and hard to understand as in deep
learning. Although there has been a growing interest in using deep learning
methods in diffusion-weighted MRI, prior works have not addressed the issue of
model uncertainty. Here, we propose a deep learning method to estimate the
diffusion tensor and compute the estimation uncertainty. Data-dependent
uncertainty is computed directly by the network and learned via loss
attenuation. Model uncertainty is computed using Monte Carlo dropout. We also
propose a new method for evaluating the quality of predicted uncertainties. We
compare the new method with the standard least-squares tensor estimation and
bootstrap-based uncertainty computation techniques. Our experiments show that
when the number of measurements is small the deep learning method is more
accurate and its uncertainty predictions are better calibrated than the
standard methods. We show that the estimation uncertainties computed by the new
method can highlight the model's biases, detect domain shift, and reflect the
strength of noise in the measurements. Our study shows the importance and
practical value of modeling prediction uncertainties in deep learning-based
diffusion MRI analysis.
