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Signal variability in diffusion weighted imaging (DWI) is influenced by both thermal noise and spatially and temporally varying artifacts such as subject motion and cardiac pulsation. In this paper, the effects of DWI artifacts on estimated tensor values, such as trace and fractional anisotropy, are analyzed using Monte Carlo simulations. A novel approach for robust diffusion tensor estimation, called RESTORE (for robust estimation of tensors by outlier rejection), is proposed. This method uses iteratively reweighted least‐squares regression to identify potential outliers and subsequently exclude them. Results from both simulated and clinical diffusion data sets indicate that the RESTORE method improves tensor estimation compared to the commonly used linear and nonlinear least‐squares tensor fitting methods and a recently proposed method based on the Geman–McClure M‐estimator. The RESTORE method could …