  Fiber tractography is an important tool of computational neuroscience that
enables reconstructing the spatial connectivity and organization of white
matter of the brain. Fiber tractography takes advantage of diffusion Magnetic
Resonance Imaging (dMRI) which allows measuring the apparent diffusivity of
cerebral water along different spatial directions. Unfortunately, collecting
such data comes at the price of reduced spatial resolution and substantially
elevated acquisition times, which limits the clinical applicability of dMRI.
This problem has been thus far addressed using two principal strategies. Most
of the efforts have been extended towards improving the quality of signal
estimation for any, yet fixed sampling scheme (defined through the choice of
diffusion-encoding gradients). On the other hand, optimization over the
sampling scheme has also proven to be effective. Inspired by the previous
results, the present work consolidates the above strategies into a unified
estimation framework, in which the optimization is carried out with respect to
both estimation model and sampling design {\it concurrently}. The proposed
solution offers substantial improvements in the quality of signal estimation as
well as the accuracy of ensuing analysis by means of fiber tractography. While
proving the optimality of the learned estimation models would probably need
more extensive evaluation, we nevertheless claim that the learned sampling
schemes can be of immediate use, offering a way to improve the dMRI analysis
without the necessity of deploying the neural network used for their
estimation. We present a comprehensive comparative analysis based on the Human
Connectome Project data. Code and learned sampling designs aviliable at
https://github.com/tomer196/Learned_dMRI.
