Mapping structural brain connectomes for living human brains typically requires expert analysis and rule-based models on diffusion-weighted magnetic resonance imaging. A data-driven approach, however, could overcome limitations in such rulebased approaches and improve precision mappings for individuals. In this work, we explore a framework that facilitates applying learning algorithms to automatically extract brain connectomes. Using a tensor encoding, we design an objective with a

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... izer that prefers biologically plausible fascicle structure. We show that the objective is convex and has a unique solution, ensuring identifiable connectomes for an individual. We develop an efficient optimization strategy for this extremely high-dimensional sparse problem, by reducing the number of parameters using a greedy algorithm designed specifically for the problem. We show that this greedy algorithm significantly improves on a standard greedy algorithm, called Orthogonal Matching Pursuit. We conclude with an analysis of the solutions found by our method, showing we can accurately reconstruct the diffusion information while maintaining contiguous fascicles with smooth direction changes.