Diffusion-weighted imaging (DWI) allows to probe tissue microstructure non-invasively and study healthy and diseased white matter (WM) in vivo. Yet, less research has focussed on modelling grey matter (GM), cerebrospinal fluid (CSF) and other tissues. Here, we introduce a fully data-driven approach to spherical deconvolution, based on convex non-negative matrix factorization. Our approach decomposes multi-shell DWI data, represented in the basis of spherical harmonics, into tissuespecific

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... ation distribution functions and corresponding response functions. We evaluate the proposed method in phantom simulations and in vivo brain images, and demonstrate its ability to reconstruct WM, GM and CSF, unsupervised and solely relying on DWI.