An Optimal Dimensionality Sampling Scheme on the Sphere with Accurate and Efficient Spherical Harmonic Transform for Diffusion MRI


We tend to design a sampling theme on the sphere and a corresponding spherical harmonic transform (SHT) for the measurement and reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry property of the diffusion signal within the spectral (spherical harmonic) domain, we have a tendency to design a sampling scheme that attains the optimal range of samples, equal to the degrees of freedom needed to represent the antipodally symmetric band-limited diffusion signal in the spectral domain. Compared with other sampling schemes that may be used with the optimal range of samples, we have a tendency to demonstrate, through numerical experiments, that the proposed theme permits a lot of accurate computation of the SHT, and this accuracy is practically rotationally invariant. Additionally, it leads to additional efficient computation of the SHT and storage of the diffusion signal.

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