An Optimal Dimensionality Multi-shell Sampling Scheme with Accurate and Efficient Transforms for Diffusion MRI

摘要

This paper proposes a multi-shell sampling scheme and correspondingtransforms for the accurate reconstruction of the diffusion signal in diffusionMRI by expansion in the spherical polar Fourier (SPF) basis. The samplingscheme uses an optimal number of samples, equal to the degrees of freedom ofthe band-limited diffusion signal in the SPF domain, and allows forcomputationally efficient reconstruction. We use synthetic data sets todemonstrate that the proposed scheme allows for greater reconstruction accuracyof the diffusion signal than the multi-shell sampling schemes obtained usingthe generalised electrostatic energy minimisation (gEEM) method used in theHuman Connectome Project. We also demonstrate that the proposed sampling schemeallows for increased angular discrimination and improved rotational invarianceof reconstruction accuracy than the gEEM schemes.