RESTORE: Robust estimation of tensors by outlier rejection

Abstract

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. Diffusion tensor magnetic resonance imaging (DT-MRI) is used increasingly in clinical research for its ability to depict white matter tracts and for its sensitivity to microstructural and architectural features of brain tissue. Diffusion tensor maps are typically computed by fitting the signal intensities from diffusion weighted images as a function of their corresponding b-matrices (1) according to the multivariate least-squares regression model proposed by Basser et al. (2). The least-squares (LS) regression model takes into account the signal variability produced by thermal noise by including the assumed signal variance as a weighting factor in the tensor fitting. Signal variability in diffusion weighted imaging (DWI), however, is influenced not only by thermal noise but also by spatially and temporally varying artifacts. Such artifacts originate from the so called "physiologic noise" such as subject motion and cardiac pulsation, as well as from acquisition-related factors such as system instabilities. The multivariate leastsquares regression model assumes that the signal variability in the DWI is affected only by thermal noise and does not account for signal perturbations and potential outliers that originate from artifacts. While the signal variability produced by thermal noise is approximately Gaussian distributed (3), signal variability produced by physiologic noise and other artifacts does not have a known parametric distribution and currently cannot be modeled. Situations in which experimental errors do not follow a Gaussian distribution, or are unknown, are generally addressed statistically by using "robust" estimators, which are less sensitive to the presence of outliers.Surprisingly, the use of robust estimators has been largely neglected by the DT-MRI community. We are aware of only one robust tensor estimation approach recently proposed by Mangin et al. (4), which is based on the well-known Geman-McClure M-estimator (5) (we will refer to Mangin's approach as GMM in this paper). This approach uses an iteratively reweighted least-squares fitting in which the weight of each data point is set to a function of the residuals of the previous iteration. The GMM method ensures that potentially artifactual data points having large residuals are given lower weights in the estimation of the tensor parameters. Clearly, this approach is statistically more robust than the standard LS methods in the presence of outl...

Minimum spanning tree analysis of the human connectome

“…The DWI set was corrected for eddy‐current distortions and small head movements by realigning all scans to the diffusion‐unweighted image (Andersson and Skare, 2002). The diffusion tensors where obtained using M‐estimators to limit the influence of possible outliers (Chang, Jones, & Pierpaoli, 2005). …”

Structural network analysis of brain development in young preterm neonates

“…Each diffusion weighted image set was preprocessed using the FSL Diffusion Toolbox (FDT) pipeline 1 and tensors were fit using RESTORE [14].…”

Altered Interhemispheric and Temporal Lobe White Matter Microstructural Organization in Severe Chronic Schizophrenia

“…ExploreDTI (Leemans A JB and Jones, 2009) was used to process the diffusion MRI data and consisted of the following steps: (i) correction for motion and eddy current induced geometric distortions with rotation of the b-matrix to ensure the orientation information is correctly preserved ); (ii) estimation of the diffusion tensor using a robust nonlinear regression method (Chang et al, 2005); and (iii) calculation of FA, AD, and RD maps. Subsequently, voxel-based statistical analysis was carried out using the tract-based spatial statistics (TBSS) approach (Smith et al, 2006) as follows: FA images were nonlinearly registered using FNIRT (Anderson et al, 2007) to the MNI152 standard space, resulting in a standard space version of each individual FA image.…”