We estimate microstructural features of the nervous tissues from diffusion-weighted MRI by using sparse optimization techniques on a dictionary of pre-computed Monte Carlo signals, which more faithfully describe the complex diffusion process in the extra-axonal space of the white matter. The method is validated on synthetic data including single and crossing fibers and on an in vivo rat spinal cord model of Wallerian degeneration. We obtain in vivo microstructural estimates that can be directly related to histological evidence whereas the traditional closed-form formula models DIAMOND and NODDI yield results that are more challenging to interpret physically.
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