Diffusion Kurtosis Imaging estimator

Diffusion tensor and parameters estimation from the DWI data, based on Tabesh et al. (2011)

These functions are a simple implementation of the algorithm presented by Tabesh et al. (2011) to estimate Diffusion Kurtosis Imaging tensors and parameters. It should be compatible with any MATLAB version after 2014, and it can be easily adapted to at least 2012 by uncommenting a line.
Provided you have data acquired in at least 15 directions, the DKI script should handle any combination of b-values and directions and return diffusion and kurtosis tensors along with the resnorm evaluating the fit's quality. To improve the estimation of diffusion parameters from the DKI-derived diffusion tensor D a constant term has been added. This does not affect the kurtosis tensor, since it regards variation of an higher order.

The DKIPAR script on the other hand uses the diffusional tensors to compute the most used diffusional and kurtosis parameters: MD, FA, AK, RK, MK. Keep in mind that MD and FA extracted from this diffusion tensor D will be different from those extracted from DTI (for example if you are using FSL), which does not separate second order effects. This script uses Carlson's integrals as implemented by Thomas Hoffend ( https://it.mathworks.com/matlabcentral/fileexchange/3705-elliptic-integrals-zip ).

No pre-processing or smoothing is applied in these scripts. These scripts can be run in parallel to improve the overall speed, which can be further improved by lowering convergence tolerance for the iterative algorithm, or by adapting them for a specific set of direction and skipping the initial controls in the DKI script. The quality of the results can be greatly improved with the right denoising method.

As of the time of writing this, the most effective strategy I am aware of employs the techniques published by Veraart et al. (2016) and Kellner et al. (2016).