Toward global tractography

•Diffusion-based tractography is an ill-posed problem.•Modeling tractography as a global inverse problem is a way to regularize the problem.•Tractography in the neighborhood of ambiguous diffusion profiles helps to infer fiber directions.

Diffusion-based tractography is an ill-posed problem, because the step-by-step reconstruction of a fibre bundle trajectory cannot afford any serious mistake in the evaluation of the local fibre orientations. Such evaluation is difficult, however, because the myriad fibres passing through a single voxel follow different directions. Modelling tractography as a global inverse problem is a simple framework which addresses the ill-posed nature of the problem. The key idea is that the results of tractography in the neighbourhood of an ambiguous local diffusion profile can help to infer the local fibre directions. This paper provides an overview of past achievements of global tractography and proposes guidelines for a future research programme in the hope that the potential of the technique will increase the interest of the community.

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