An Optimal Dimensionality Sampling Scheme on the Sphere with Accurate and Efficient Spherical Harmonic Transform for Diffusion MRI
An Optimal Dimensionality Sampling Scheme on the Sphere with Accurate and Efficient Spherical Harmonic Transform for Diffusion MRI
复制标题
一种用于扩散MRI的精确高效球谐变换球体最优维数采样方案
DOI：
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发表时间：
2016
影响因子：
3.9
通讯作者：
R. Kennedy
中科院分区：
文献类型：
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作者：
Alice P. Bates;Z. Khalid;R. Kennedy
设计了球面上的采样方案和相应的球面调和变换(SHT)，用于扩散磁共振成像(DMRI)中扩散信号的测量和重建。通过利用扩散信号在谱(球谐)域中的对极对称性，我们设计了一种采样方案，该方案获得了最佳样本数目，等于在谱域中表示对极对称带限扩散信号所需的自由度。通过数值实验证明，与其他采样方案相比，本文提出的采样方案能够更准确地计算SHT，而且精度几乎是旋转不变的。此外，它还导致了更有效的SHT计算和扩散信号的存储。
We design a sampling scheme 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 in the spectral (spherical harmonic) domain, we design a sampling scheme that attains the optimal number of samples, equal to the degrees of freedom required to represent the antipodally symmetric band-limited diffusion signal in the spectral domain. Compared with other sampling schemes that can be used with the optimal number of samples, we demonstrate, through numerical experiments, that the proposed scheme enables more accurate computation of the SHT, and this accuracy is practically rotationally invariant. In addition, it results in more efficient computation of the SHT and storage of the diffusion signal.