  Diffusion kurtosis imaging is an extension of diffusion tensor imaging that
provides scientifically and clinically valuable information about brain tissue
microstructure but suffers from poor robustness to noise, especially in voxels
containing tightly packed aligned axons. We present a new algorithm for
estimating diffusion and kurtosis tensors using regularized non-linear
optimization and make it publicly available in an easy-to-use open-source
Python software package. Our approach uses fully-connected feed-forward neural
networks to predict kurtosis values in voxels where the standard non-linear
least squares fit fails. The predicted values are then used in the objective
function to avoid implausible kurtosis values. We show that our algorithm is
more robust than standard non-linear least squares and a previously proposed
regularized non-linear optimization method. The algorithm was then applied on a
multi-site scan-rescan dataset acquired using a clinical scan protocol to
assess the reproducibility of diffusion kurtosis parameter estimation in human
white matter using the proposed algorithm. Our results show that the
reproducibility of diffusion kurtosis parameters is similar to diffusion tensor
parameters.
