Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA.
Neuroimage. 2017 Nov 1;161:206-218. doi: 10.1016/j.neuroimage.2017.08.048. Epub 2017 Aug 19.
The data measured in diffusion MRI can be modeled as the Fourier transform of the Ensemble Average Propagator (EAP), a probability distribution that summarizes the molecular diffusion behavior of the spins within each voxel. This Fourier relationship is potentially advantageous because of the extensive theory that has been developed to characterize the sampling requirements, accuracy, and stability of linear Fourier reconstruction methods. However, existing diffusion MRI data sampling and signal estimation methods have largely been developed and tuned without the benefit of such theory, instead relying on approximations, intuition, and extensive empirical evaluation. This paper aims to address this discrepancy by introducing a novel theoretical signal processing framework for diffusion MRI. The new framework can be used to characterize arbitrary linear diffusion estimation methods with arbitrary q-space sampling, and can be used to theoretically evaluate and compare the accuracy, resolution, and noise-resilience of different data acquisition and parameter estimation techniques. The framework is based on the EAP, and makes very limited modeling assumptions. As a result, the approach can even provide new insight into the behavior of model-based linear diffusion estimation methods in contexts where the modeling assumptions are inaccurate. The practical usefulness of the proposed framework is illustrated using both simulated and real diffusion MRI data in applications such as choosing between different parameter estimation methods and choosing between different q-space sampling schemes.
扩散 MRI 测量的数据可以建模为集合平均传播算子（EAP）的傅里叶变换，EAP 是一种概率分布，总结了每个体素内自旋的分子扩散行为。这种傅里叶关系具有潜在的优势，因为已经开发出了广泛的理论来描述线性傅里叶重建方法的采样要求、准确性和稳定性。然而，现有的扩散 MRI 数据采样和信号估计方法在很大程度上是在没有这种理论的情况下开发和调整的，而是依赖于近似、直觉和广泛的经验评估。本文旨在通过引入一种新的扩散 MRI 理论信号处理框架来解决这一差异。新框架可用于描述具有任意 q 空间采样的任意线性扩散估计方法，并可用于从理论上评估和比较不同数据采集和参数估计技术的准确性、分辨率和抗噪能力。该框架基于 EAP，并且做出了非常有限的建模假设。因此，即使在建模假设不准确的情况下，该方法也可以为基于模型的线性扩散估计方法的行为提供新的见解。该框架的实际用途通过在不同参数估计方法之间进行选择和在不同 q 空间采样方案之间进行选择等应用中使用模拟和真实扩散 MRI 数据进行了说明。
