Cramer-Rao bounds for three-point decomposition of water and fat
Cramer-Rao bounds for three-point decomposition of water and fat
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DOI：
10.1002/mrm.20623
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发表时间：
2005-09-01
影响因子：
3.3
通讯作者：
Pelc, NJ
中科院分区：
文献类型：
--
作者：
Pineda, AR;Reeder, SB;Pelc, NJ
对水和脂肪三点分解的噪声分析进行了扩展，以考虑野外图中的不确定性。这种泛化导致了一个非线性估计问题。Cramer-Rao界（CRB）通过计算任何选择的回波时移的最大有效平均信号数（NSA）来研究幅度、相位和场图估计的方差。分析表明，重建的幅值、相位和场图的噪声特性不仅与回波时移的选择有关，还与每个体素中脂肪和水的数量及其在回波处的排列有关。利用CRB优化了自旋回波、破坏梯度回波和稳态自由进动成像技术的回波时移选择。噪声分析的幅度解释了临床上在脂肪和水的边界上看到的粗糙界面与自旋回波对称的源图像。它还提供了一个解决方案，通过选择适当的回波时移（-pi/6 + pi k, pi/2 + pi k, 7 pi/6 + pi k），其中k为整数。有了这种回声时移的选择，就有可能在所有脂肪：水比中均匀地获得最大的NSA。对相位图和场图的估计也进行了优化。通过蒙特卡罗模拟验证了这些理论结果，并采用了一种新开发的非线性最小二乘重构算法来实现CRB。
The noise analysis for three-point decomposition of water and fat was extended to account for the uncertainty in the field map. This generalization leads to a nonlinear estimation problem. The Cramer-Rao bound (CRB) was used to study the variance of the estimates of the magnitude, phase, and field map by computing the maximum effective number of signals averaged (NSA) for any choice of echo time shifts. The analysis shows that the noise properties of the reconstructed magnitude, phase, and field map depend not only on the choice of echo time shifts but also on the amount of fat and water in each voxel and their alignment at the echo. The choice of echo time shifts for spin-echo, spoiled gradient echo, and steady-state free precession imaging techniques were optimized using the CRB. The noise analysis for the magnitude explains rough interfaces seen clinically in the boundary of fat and water with source images obtained symmetrically about the spin-echo. It also provides a solution by choosing appropriate echo time shifts (-pi/6 + pi k, pi/2 + pi k, 7 pi/6 + pi k), with k an integer. With this choice of echo time shifts it is possible to achieve the maximum NSA uniformly across all fat:water ratios. The optimization is also carried out for the estimation of phase and field map. These theoretical results were verified using Monte Carlo simulations with a newly developed nonlinear least-squares reconstruction algorithm that achieves the CRB.