Theoretical analysis of the effects of noise on diffusion tensor imaging
Theoretical analysis of the effects of noise on diffusion tensor imaging
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DOI：
10.1002/mrm.1315
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发表时间：
2001-12-01
影响因子：
3.3
通讯作者：
Anderson, AW
中科院分区：
文献类型：
--
作者：
Anderson, AW
提出了一个理论框架，以了解噪声的影响，估计的特征值和特征向量的扩散张量在中等到高的信噪比。图像噪声产生扩散张量的随机扰动。本征值方程的幂级数解用于评估二阶扰动的影响。结果表明，在各向异性系统中，最大本征值的期望值被高估，最小本征值被低估。因此，扩散各向异性一般被高估。这一结果与特征值排序偏差无关。此外，在感兴趣的区域上平均特征值比对角化之前平均张量产生更大的偏差。最后，本征向量噪声取决于本征值的对比度，并对简单的光纤跟踪计划的准确性施加了理论限制。理论结果与Monte Carlo模拟结果一致。(C)2001 Wiley-Liss，Inc.
A theoretical framework is presented for understanding the effects of noise on estimates of the eigenvalues and eigenvectors of the diffusion tensor at moderate to high signal-to-noise ratios. Image noise produces a random perturbation of the diffusion tensor. Power series solutions to the eigenvalue equation are used to evaluate the effects of the perturbation to second order. It is shown that in anisotropic systems the expectation value of the largest eigenvalue is overestimated and the lowest eigenvalue is underestimated. Hence, diffusion anisotropy is overestimated in general. This result is independent of eigenvalue sorting bias. Furthermore, averaging eigenvalues over a region of interest produces greater bias than averaging tensors prior to diagonalization. Finally, eigenvector noise is shown to depend on the eigenvalue contrast and imposes a theoretical limit on the accuracy of simple fiber tracking schemes. The theoretical results are shown to agree with Monte Carlo simulations. (C) 2001 Wiley-Liss, Inc.