Mean apparent propagator (MAP) reconstructs the diffusion pdf using a dictionary based on Hermite functions. The first element corresponds to a tensor approximation; and the following elements add non-gaussian components. To improve non-gaussian accuracy, one needs to increase the size of the dictionary, but it also increases the number of q-space samples for a robust optimisation. We propose the use of compressed sensing to efficiently increase the number of atoms in the dictionary by exploiting its sparsity for a better reconstruction.
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