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## Section: New Results

### Reducing the number of samples in spatiotemporal dMRI acquisition design

Acquisition time is a major limitation in recovering brain white matter microstructure with diffusion magnetic resonance imaging. The aim of this work is to bridge the gap between growing demands on spatio-temporal resolution of diffusion signal and the real-world time limitations. We introduce an acquisition scheme that reduces the number of samples under adjustable quality loss. Finding a sampling scheme that maximizes signal quality and satisfies given time constraints is NP-hard. Therefore, a heuristic method based on genetic algorithm is proposed in order to find sub-optimal solutions in acceptable time. The analyzed diffusion signal representation is defined in the qτ space, so that it captures both spacial and temporal phenomena. The experiments on synthetic data and in vivo diffusion images of the C57Bl6 wild-type mouse corpus callosum reveal the superiority of the proposed approach over random sampling and even distribution in the qτ space. The use of genetic algorithm allows to find acquisition parameters that guarantee high signal reconstruction accuracy under given time constraints. In practice, the proposed approach helps to accelerate the acquisition for the use of q-dMRI signal representation.

Figure 3. Exhaustive search results of the optimization by shells for the in silico experiment with nmax = 100. The plots at the top present all the 658,008 feasible acquisition schemes arranged from best to worst, illustrating the mean squared errors (MSEs) of signal reconstruction (top-left plot) and the normalized Hamming distances from the global optimum ± 1 standard deviation (top-right). In order to visualize the analyzed (G, $\Delta$) parameter space, the percentiles pc = 0%, 1%, 10%, 50%, 90% are annotated on both plots, showing respectively the global optimum, the top 1% solutions, the top 10% solutions, etc. The corresponding cumulative averages of acquisition schemes are depicted in the heat maps at the bottom. The colors reflect the likelihood of a given (G, $\Delta$) pair in the scheme. The heat maps for pc ≤ 0% and pc ≤ 1% represent, respectively, the global optimum and its proximity. The interval between pc = 10% and pc = 90% contains a huge spectrum of schemes with similar MSEs and almost equally large distances from the global optimum.