We propose and validate a data cleaning strategy for arterial spin labeling data.Arterial Spin Labeling (ASL)¹ provides non-invasive quantification of regional cerebral blood flow (CBF). It’s characteristic low signal to noise ratio (SNR) is compensated by acquiring and signal averaging multiple tag-control pairs. However the process is often undermined by large spatially constrained artifacts present in some or potentially all of the CBF volumes in the time series. In ², we proposed structural correlation based outlier rejection (SCORE) for detecting and discarding outlier volumes contributing to the artifacts. However, it is based on either keeping or discarding an entire CBF volume in the time series. Some volumes are also retained to improve SNR at the expense of preserving the artifact. Hence further improvement is potentially feasible based on signal processing on individual voxel level. In this abstract, we propose Structural Correlation with RobUst Bayesian (SCRUB) estimation, an Empirical Robust Bayesian approach on the voxels after application of SCORE.SCRUB is compared with simple average (SA), mean and standard deviation based filter (MSD),³ Huber’s M Estimation (HME) ⁴ and SCORE using pulsed ASL data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) study (http://adni.loni.usc.edu). The superiority of SCRUB is demonstrated by (i) visual comparison and by comparing (ii) variability in mean CBF in several regions of interest (ROIs) from ASL data acquired 3 months apart, measured using coefficient of variation (CV), for 52 control subjects, and (iii) ability to differentiate 61 Controls and 49 AD patients by comparing the effect sizes in hippocampus, posterior cingulate cortex (PCC) and precuneus, which are sensitive to AD related changes.⁵ For preprocessing, raw label-control time series were motion corrected,⁶ and then the CBF time series were estimated following the model in ⁷. Separately acquired T1 weighted MPRAGE images were segmented to obtain tissue probability maps (TPMs) for grey matter (GM), white matter (WM) and cerebrospinal fluid (CSF), and then coregistered to the native space for use in SCRUB.

SCRUB consists of (i) SCORE and (ii) a subsequent empirical Robust Bayesian estimation⁸ step. SCORE first discards CBF volumes, whose GM means are 2.5 standard deviation away from the median of the GM means. Thereafter it iteratively removes volumes that are most structurally correlated to the intermediate mean CBF map unless the variance within each tissue type starts increasing (which implies an effect of white noise removal as opposed to outlier rejection). Then SCRUB estimates CBF at voxel $$$(x,y,z)$$$ as $$\hat{CBF}_{x,y,z}=\arg\min_\theta \sum_{t=1}^N \rho(CBF_{x,y,z,t}-\theta)+\lambda_{x,y,z}(\theta-\mu_{x,y,z})^2\hspace{3cm}(1)$$

$$\mu_{x,y,z}=\sum_{i\in {\rm Tissue~type}}p_{x,y,z,i}\mu_i\hspace{5cm}(2)$$

$$ \lambda_{x,y,z}=\begin{cases}\eta_{x,y,z}^4 & \eta \leq1\\ 4\eta_{x,y,z}-3 & \eta > 1\end{cases}\hspace{4.5cm}(3)$$

using an iterative reweighted least square method. Here $$$CBF_{x,y,z,t}$$$ is the CBF at voxel location $$$(x,y,z)$$$ and time $$$t$$$, $$$p_{x,y,z,i}$$$ is the tissue probability of the $$$i$$$th tissue ($$$i\in$$$ {GM, WM, CSF}) at location $$$(x,y,z)$$$ and $$$\mu_i$$$ is the mean CBF for $$$i$$$th tissue estimated from SCORE output. The first term on the right hand side in Equation (1) is a data fidelity term. The second term is a prior term (Bayesian framework), which ensures that the solution is not too different from the expected value based on tissue probabilities and tissue global means. $$$\rho$$$ is set to Tukey’s bisquare function, which is less sensitive to large errors (compared to square error function) and thus imposing robustness to the solution. $$$\lambda$$$ is a weighting parameter and $$$\eta_{x,y,z}$$$ is the ratio of temporal variance at $$$(x,y,z)$$$ and the overall variance for all the voxels. Higher $$$\eta$$$ implies higher temporal variance compared to the global variance, and hence a less reliable voxel, and thus assigns more weight (higher $$$\lambda$$$) on the prior term.

Figure 1 provides visual comparison of the different reconstruction algorithms. The top row of Figure 1 demonstrates an example of artifact, which was caused by outliers and hence was corrected by SCORE itself and where SCRUB produced very similar result. The artifact in the bottom row, on the other hand, was not solely due to outlier volumes, and hence although SCORE improved the map compared to other methods, SCRUB provided a much better CBF map. Figure 2 shows the CVs (higher CV implies more disagreement between different sessions) corresponding to different ROIs. The number of subjects rejected from the calculation of combined CV because of high values (CV>$$$100\%$$$) for those subjects are shown above each bar. In each case, SCRUB provided the best reliability and also discarded the lowest number of subjects. Finally, figure 3 shows the effect sizes for Control-AD discrimination for all the algorithms. SCRUB provided better discrimination on an average for the ROIs sensitive to AD.