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D-stripe: correction for stripe artefacts in diffusion MRI using a combined deep neural network and SVR approach
Maximilian Pietsch1,2, Daan Christiaens2,3, J-Donald​ Tournier1,2, and Joseph​ V. Hajnal2,3

1​Biomedical Engineering Department, School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom, 2Centre for the Developing Brain, School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom, 3Biomedical Engineering Department, School of Biomedical Engineering and Imaging Sciences,​ ​ King’s ​ College​ ​ London, King's College London, London, United Kingdom

### Synopsis

We present a data-driven method for the correction of stripe artefacts in multi-shell diffusion data that might arise for example from spin-history or stimulated echo effects. It relies on a filter, based on a deep neural network trained with simulated data to detect and remove stripe artefacts from single volumes. This is used to destripe signal predictions obtained from a slice to volume reconstruction, which are then projected onto the input data to determine the appropriate modulation field. The corrected input data are then reconstructed again with reduced stripe artefacts. This approach is applied to super-resolution reconstructions of neonatal multi-shell high angular resolution data.

### Introduction

Diffusion MRI (dMRI) provides unique information about the microstructural properties of brain tissue. The diffusion weighting is achieved via strong motion sensitisation gradients, which poses major challenges for in-vivo imaging.

Interactions with previous pulses (spin-history effects) in interleaved EPI, variations in slice timing, stimulated echoes, and scanner hardware limitations can all lead to inter-slice inconsistencies, which can particularly destabilise super-resolution reconstruction.

Here, we present a new strategy for destriping dMRI data based on a deep neural network integrated with a slice-to-volume reconstruction (SVR) framework. This approach does not require a model of the source of the artefact, is applicable to super-resolution acquisitions1, images with slab boundary artefacts2,3,4 and variable slice-timing artefacts5, is comparatively robust to motion6.

We use the reconstructed image (Recon) as the basis for destriping because data in this space is corrected for other image artefacts, facilitating estimating slice-wise intensity modulation in the absence of distortions, dropout and misalignment due to subject motion. The intensity modulation is then back-projected to source-space, and the stripe correction applied to the input data (figure 1a).

### Methods

Data and reconstruction dMRI data were acquired in 300 volumes at $1.5\times1.5\times3mm$ resolution in 64 slices with 1.5mm slice-overlap; interleave 3, shift 2; MB=4; TR=3800ms; TE=90ms; diffusion weightings $b=[0,\,400,\,1000,\,2600]s/mm^2$ with $n=[20,\,64,\,88,\,128]$ directions, respectively7–9. Images were reconstructed to native resolution and denoised10. Field maps and brain masks were estimated with FSL topup11 and bet12.

The dMRI data was processed using an SVR motion correction and super-resolution (native slice profile) reconstruction algorithm, based on a data-driven multi-shell low-rank data representation and outlier estimation13,14.

Destripe neural network The destripe-filter consists of a convolutional neural network (figure 1c) that operates on individual $3D$ volumes. It was trained to remove simulated per-slice scale factors imprinted on reconstructed DW volumes from 6 neonates (100 training epochs) by predicting the original image volume from the corrupted input image via a multiplicative modulation-field applied to the input volume. The network uses pooling to down-sample the in-plane resolution to 16x16 points followed by linear upsampling and Gaussian smoothing ($std=7\,$voxels) of the field (figure 1c). Hence, the modulation-field is smooth in-plane. It is additionally constrained by high-pass filtering in the slice-direction to remove slowly varying bias fields and by scaling it globally to conserve the average image intensity in the brain mask, to avoid potentially shell-specific biases. This is repeated thrice to iteratively remove stripe-patterns.

Source field estimation The constrained modulation-field is applied to the motion-corrected intensity predictions, produced by projecting the reconstructed multi-shell SH image post SVR (Recon, see figure 1a), which were then converted back to spherical harmonics to obtain the filtered reconstruction (Reconfiltered). The projection of Reconfiltered to the scattered (but dropout-free) source-space yields the filtered signal predictions DWpredfiltered. These are divided by the unfiltered signal prediction (DWpred), and median-filtered in-plane (3x3-kernel) to obtain the modulation-field in source-space (Destripe field). The Destripe field is multiplied with the raw DW data (DWraw) and passed through the SVR reconstruction to obtain the final reconstruction Reconfinal (figure 1b).

### Results and discussion

An example subject with a clear stripe pattern in the super-resolution SH coefficients is shown in figure 2a). The destripe network operates on the amplitude projection of Recon, back-projected into the multi-shell basis; this shows that destriping in amplitude space has removed the majority of the stripe pattern in the SH coefficients (figure 2b) across all shells and for $\ell=0,\,2\,4$. The reconstruction of the destriped raw data (Recon final) contains residual stripe patterns (figure 2d) that can be mostly removed by repeating the destripe filtering and reconstruction thrice (figure 2e). This indicates that our approach can suppress the majority of the stripe pattern present in the raw data.

To check whether a projection to the angular domain is necessary, the destripe field was estimated from the much higher SNR shell-average terms ($\ell=0$) and then applied to all SH terms of the respective shell. This performs comparably for the $\ell=0$ coefficients, yet in this case, the angular coefficients contain significantly higher stripe artefacts (figure 2c, 2d). Hence, a projection into the angular domain is beneficial and necessary for destriping.

Figure 3 shows example source-space Destripe fields. They do not contain anatomical features and have no discernable low-frequency or global bias. Multiple iterations refine the field with decreasing amplitude, indicating convergence (figure 3b). The destriping significantly removes stripe patterns of multi-shell-based metrics (figure 4).

### Conclusion

The presented destriping technique allows the data-driven removal of slice-stripe patterns in dMRI data, without explicitly modelling the source of the stripe pattern. The iterative integration of stripe-removal and reconstruction allows estimating the slice modulation in source-space, even in the presence of motion.

### Acknowledgements

This work was supported by ERC grant agreement no. 319456 (dHCP project), the Wellcome EPSRC Centre for Medical Engineering at Kings College London (WT 203148/Z/16/Z) and by the National Institute for Health Research (NIHR) Biomedical Research Centre based at Guy’s and St Thomas’ NHS Foundation Trust and King’s College London. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health.

### References

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### Figures

Fig. 1 overview. a) Estimation of the multiplicative destripe modulation field from raw DW data. This can be repeated to refine the field. The field is applied to the input data, and the final reconstructed image is obtained after one more pass through the reconstruction (b). Destriping is performed on amplitude projections of the reconstructed image (free of dropout) via a neural network filter that estimates a multiplicative field that is smooth in-plane, constrained to avoid global and slice-wise local signal intensity drift (c). The final destripe field is estimated from the source signal prediction via back-projection of the unfiltered and filtered reconstructed images.

Fig. 2 Sagittal cross-sections through the initial reconstruction without destriping a), with the destripe filter applied in reconstruction space b) and after back-projection to source space, source-field estimation and reconstruction with modulation applied to the raw DW data c) to e). Images in c) were generated using destriping of only the $\ell=0$ terms of the reconstructed image, but the estimated shell-average field also applied to the higher harmonic terms. After reconstruction, images corrected with this field show significant residual stripe patterns in the $\ell=0$ and in higher-order SH coefficients. Columns d),e) show results after destriping using all angular projections after 1 and 3 destripe iterations.

Fig. 3 Destripe field of a single volume in source space. Shown are all spatially contiguous axial slices covering one multiband slab of the field after one destripe iteration a) and sagittal sections of the field in these volumes after the first iteration and the two multiplicative updates relative to the previous field b). The last column shows the shell-averaged multiplicative field at iteration 1. Note the smaller amplitude in the shell-averaged field, indicating that the field is not static across volumes.

Fig. 4 Comparison of maps derived from a reconstructed image without (left) and with (right) destriping. FA maps are comparable but appear slightly more consistent in the destriped reconstruction. The effect of destriping is clearly noticeable in the tissue volume fraction and free fluid maps derived via multi-shell multi-tissue CSD15,16. Image intensities in each row are scaled identically.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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