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.