Iterative reweighted linear least squares for accurate, fast, and robust estimation of diffusion magnetic resonance parameters

Purpose Diffusion‐weighted magnetic resonance imaging suffers from physiological noise, such as artifacts caused by motion or system instabilities. Therefore, there is a need for robust diffusion parameter estimation techniques. In the past, several techniques have been proposed, including RESTORE and iRESTORE (Chang et al. Magn Reson Med 2005; 53:1088–1095; Chang et al. Magn Reson Med 2012; 68:1654–1663). However, these techniques are based on nonlinear estimators and are consequently computationally intensive. Method In this work, we present a new, robust, iteratively reweighted linear least squares (IRLLS) estimator. IRLLS performs a voxel‐wise identification of outliers in diffusion‐weighted magnetic resonance images, where it exploits the natural skewness of the data distribution to become more sensitive to both signal hyperintensities and signal dropouts. Results Both simulations and real data experiments were conducted to compare IRLLS with other state‐of‐the‐art techniques. While IRLLS showed no significant loss in accuracy or precision, it proved to be substantially faster than both RESTORE and iRESTORE. In addition, IRLLS proved to be even more robust when considering the overestimation of the noise level or when the signal‐to‐noise ratio is low. Conclusion The substantially shortened calculation time in combination with the increased robustness and accuracy, make IRLLS a practical and reliable alternative to current state‐of‐the‐art techniques for the robust estimation of diffusion‐weighted magnetic resonance parameters. Magn Reson Med 73:2174–2184, 2015. © 2014 Wiley Periodicals, Inc.