We propose a 4-dimensional (4D) basis and sampling scheme, along with a corresponding reconstruction algorithm, for the measurement and reconstruction of the $\mathbf {b}$-tensor encoded diffusion signal in diffusion magnetic resonance imaging (MRI). This is only the second basis proposed for representing the $\mathbf {b}$-tensor encoded diffusion signal and the first to allow for planar tensor measurements. We design a sampling scheme that attains an efficient number of samples, equal to the degrees of freedom required to represent the diffusion signal in the proposed 4D basis. The properties of the diffusion signal are studied to provide recommendations on how many $\mathbf {b}$-tensor measurements to use. Evaluation of the proposed scheme using Monte Carlo simulations of the diffusion signal is done to show that the proposed scheme gives accurate interpolation of the signal.

中文翻译：

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张量编码的多维扩散 MRI 信号的 4D 基础和采样方案

我们提出了一个 4 维 (4D) 基础和采样方案，以及相应的重建算法，用于测量和重建 $\mathbf {b}$- 扩散磁共振成像 (MRI) 中的张量编码扩散信号。这只是为代表提出的第二个依据$\mathbf {b}$-张量编码扩散信号，第一个允许平面张量测量。我们设计了一个采样方案，可以获得有效数量的样本，等于在建议的 4D 基础中表示扩散信号所需的自由度。研究了扩散信号的特性，以提供关于有多少$\mathbf {b}$- 要使用的张量测量。使用扩散信号的蒙特卡罗模拟对所提出的方案进行评估，以表明所提出的方案给出了信号的准确插值。