扩散磁共振成像中对映信号的球面上最优离散采样方案
An Optimal Dimensionality Sampling Scheme on the Sphere for Antipodal Signals In Diffusion Magnetic Resonance Imaging
摘要：
提出了一种球面采样方案，并提出了一种相应的球面谐波变换（SHT），用于弥散磁共振成像（dMRI）中弥散信号的精确重建。通过利用对映对称性，我们设计了一个采样方案，需要在球体上的样本的最佳数量，等于所需的自由度来表示谱域（球谐）域中的对映对称带限扩散信号。与现有的采样方案上的球，允许扩散信号的准确重建相比，所提出的采样方案减少了所需的样本的数量的两个或更多的因素。我们分析了所提出的SHT的数值精度，并通过实验表明，所提出的采样允许SHT的准确和旋转不变的计算，以接近机器的精度精度。
英文摘要：
We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry, we design a sampling scheme that requires the optimal number of samples on the sphere, equal to the degrees of freedom required to represent the antipodally symmetric band-limited diffusion signal in the spectral (spherical harmonic) domain. Compared with existing sampling schemes on the sphere that allow for the accurate reconstruction of the diffusion signal, the proposed sampling scheme reduces the number of samples required by a factor of two or more. We analyse the numerical accuracy of the proposed SHT and show through experiments that the proposed sampling allows for the accurate and rotationally invariant computation of the SHT to near machine precision accuracy.
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