A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging
A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging
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DOI：
10.1016/j.jmr.2006.06.020
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发表时间：
2006-09-01
影响因子：
2.2
通讯作者：
Basser, Peter J.
中科院分区：
文献类型：
--
作者：
Koay, Cheng Guan;Chang, Lin-Ching;Basser, Peter J.
提出了扩散张量估计的统一理论和算法框架。线性最小二乘法(LLS)、加权线性最小二乘法(WLLS)、非线性最小二乘法(NLS)及其约束最小二乘法之间的理论联系是通过它们各自的目标函数以及这些目标函数的高阶导数，即海森矩阵来建立的。这些理论联系为设计有效的NLS和约束NLS(CNLS)估计算法提供了新的见解。在这里，我们提出了新的完全牛顿型算法来估计NLS和CNLS，并用蒙特卡罗模拟进行了评估，并与常用的Lvenberg-MarQuardt方法进行了比较。与Levenberg-MarQuardt方法相比，该方法估计迹的相对误差百分比更低，约化X(2)值更小。这些结果还表明，估计的精度，特别是在非线性估计问题中，很大程度上受Hessian矩阵的影响。换句话说，非线性估计的准确性取决于算法。进一步研究表明，当信噪比(SNR)较低时，扩散加权信号中的噪声方差与方向有关。
A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi(2) value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (