A Novel Spatial-Angular Domain Regularisation Approach for Restoration of Diffusion MRI

In this paper we tackle the problem of regularisation for inverse problems in single shell diffusion weighted image restoration. Our aim is to recover a high-resolution and denoised DWI signal, prior to any model fitting. The main contribution of our method is the combination of two regularization terms, one using the information arising from the spatial domain, hence analysing the single image, while the other uses information coming from the angular domain, thus using the relationships between the values along different directions within a single voxel. We show that our novel regularization method outperforms widely used and recent DWI denoising algorithms. Additionally we demonstrate that the proposed regularisation technique can be successfully applied to the super-resolution reconstruction of high-resolution volume from thick-slice data. Both scenarios are tested on simulated phantom and real DWI data.