Daan Christiaens^{1,2}, Lucilio Cordero-Grande^{1,2}, Joseph V Hajnal^{1,2}, and J-Donald Tournier^{1,2}

Detecting and downweighting damaged slices is vital in analysing motion-corrupted dMRI data. Conventional magnitude-based outlier rejection methods rely on intensity model predictions, with the state of the art using slice-to-volume reconstruction. However, in cases with very high outlier prevalence such model prediction is no longer reliable. Here, we introduce a model-independent phase-based measure for detecting motion-induced slice dropouts. We demonstrate its use in neonatal data, and show that it outperforms model-based magnitude techniques in highly damaged data.

Diffusion MRI (dMRI) can probe tissue microstructure in vivo using pulsed gradient encoding that sensitizes the signal to water self-diffusion. In standard EPI-based dMRI sequences subject motion, particularly during the diffusion preparation, can cause signal dropouts at the slice or multiband excitation level ^{1}. Detecting these slice dropouts as outliers and downweighting or rejecting them in slice-to-volume reconstruction and/or local modelling can substantially improve the quality of subsequent dMRI analysis ^{2}.

Outlier rejection strategies typically compare the measured signal magnitude to an intensity model prediction. However, when there is a high incidence of corrupted slices the fitted model may become less reliable and in low SNR regimes, detecting a significant signal difference from a model prediction can be less effective. Here, we introduce a model-independent outlier measure derived from the phase images of the EPI slice, and demonstrate its use in neonatal dMRI data.

**Data:** Neonatal dMRI data of the Developing Human Connectome Project were acquired on a Philips 3T Achieva system with a 32-channel neonatal head coil ^{3}; resolution 1.5x1.5x3mm with 1.5mm slice overlap; MB=4; SENSE=1.2; *b*=0(20), 400(64), 1000(88), 2600(128) s/mm^{2}. Data were preprocessed with image denoising ^{4} and Gibbs ringing correction ^{5}, and a B_{0} field map was estimated using FSL Topup ^{6}.

**Magnitude-based measure:** Magnitude-based outlier rejection requires an intensity model prediction, provided in this case by a slice-to-volume reconstruction (SVR) framework ^{7}. In SVR, a motion-free signal representation and rigid motion parameters for each slice are jointly optimized in the reconstruction.

In this process, a signal prediction for each slice is compared to the measured intensity using the root-mean-squared error. Per-excitation outlier probabilities are then derived in a 2-class mixture model of log-normal distributions, evaluated per *b*-value shell (Fig.1). Note that these probabilities need to be updated in each iteration of the SVR process.

**Phase-based measure:** Subject motion leaves an imprint on the phase of diffusion-weighted images in each slice or multiband excitation: translation induces a phase offset and rotation induces a linear phase ramp (Fig.2). This leads to the following relation between the uncorrupted *k*-space signal $$$S(k_x,k_y)$$$ and the measured spectrum $$$S'(k_x,k_y)$$$ in each slice: $$S'(k_x,k_y) = e^{d\phi} S(k_x + dk_x, k_y + dk_y)\quad,$$ where $$$d\mathbf{k}$$$ is a shift in *k*-space (linear phase ramp) about the diffusion gradient and $$$d\phi$$$ is the phase offset ^{8}. $$$d\mathbf{k}$$$ and $$$d\phi$$$ are proportional to the respective rotation and translation, and also to the diffusion gradient strength $$$\|\mathbf{G}\| \propto \sqrt{b}$$$.

The linear phase component in each slice can hence provide an independent measure of motion. Here, we measure the linear phase by detecting the peak of the power spectrum. We heuristically define the *inlier* probability as a Gaussian PDF of the offset $$$\|d\mathbf{k}\|$$$, scaled by the b-value: $$P_i = \mathcal{N}(\|d\mathbf{k}\|; 0, b\,\sigma^2)\quad,$$ where the scale $$$\sigma$$$ is a tunable constant, here set to 0.05. We can then downweight or reject slices with low inlier probability.

**Combined measure:** We also combine both by using the phase-based outlier probability as prior for the magnitude-based method. Upon each SVR iteration, the updated magnitude-based inlier probability is multiplied with the fixed phase-based inlier probability.

Fig.3 shows the detected phase at the peak of the power spectrum (intercept) and the distance of the peak location to the k-space centre (slope). We observe that while the intercept provides little usable information, the slope shows a clear pattern that coincides with subject motion and with the magnitude-based outlier detection (Fig.1).

Figures 4 and 5 show the effect of the different strategies on SVR when using the slice inlier probability for weighted least-squares reconstruction. The left column shows the need for outlier rejection in the selected volumes. The other columns show the SVR result with the reference magnitude-based outlier rejection method, the independent phase-based measure, and the combined method. In the large majority of subjects, as exemplified in Fig.4, all measures deliver good, on par results. However, in extreme cases (Fig.5), the phase-based and combined measures can recover highly outlier-corrupted data where magnitude-based methods fail.

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