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We use a multidimensional signal representation that inte- grates diffusion Magnetic Resonance Imaging (dMRI) and tractography (brain connections) using sparse tensor decomposition. The representa- tion encodes brain connections (fibers) into a very-large, but sparse, core tensor and allows to predict dMRI measurements based on a dictionary of diffusion signals. We propose an algorithm to learn the constituent parts of the model from a dataset. The algorithm assumes a tractography model (support of core tensor) and iteratively minimizes the Frobenius norm of the error as a function of the dictionary atoms, the values of nonzero entries in the sparse core tensor and the fiber weights. We use a nonparametric dictionary learning (DL) approach to estimate signal atoms. Moreover, the algorithm is able to learn multiple dictionaries associated to different brain locations (voxels) allowing for mapping distinctive tissue types. We illustrate the algorithm through results obtained on a large in-vivo high-resolution dataset.