Frobenius optimization of tensor-valued diffusion sampling schemes
Alexis Reymbaut1
1Random Walk Imaging AB, Lund, Sweden
We derive a sampling scheme optimization strategy based on maximizing the Frobenius distance between b-tensors, thereby maximizing the diversity of probed diffusion patterns. Its evaluation in silico demonstrates that it increases the accuracy of diffusion tensor distribution imaging.
Fig.2: Acquisition schemes presented used in this work, presented as a set of b-value ($$$b$$$) and b-shape ($$$b_\Delta$$$) shells. For the platonic-solid sampling scheme, b-tensor directions sets are shown as black dots (electrostatic repulsion)8,9 or colored dots (platonic solids).15,16 Other sampling schemes feature unspecific blue dots for directions. The conventional electrostatic sampling scheme was generated by setting the intra/inter shell optimization strength from Ref.[9] to $$$\alpha=0.75$$$.
Fig.3: Histograms showing the median and interquartile range over 50 Rician noise realizations at signal-to-noise ratio SNR=30 of the DTD statistical descriptors of interest estimated in the numerical systems of Fig.1 using the acquisition schemes of Fig.2, namely the electrostatic ("Elst.", blue), platonic-solid ("Plat.", green) and Frobenius-optimized ("Frob.", red) schemes. Purple lines: ground-truth values.