Pineda Angel R, Reeder Scott B, Wen Zhifei, Pelc Norbert J
Department of Radiology, Stanford University Medical Center, Stanford, California 94305, USA.
Magn Reson Med. 2005 Sep;54(3):625-35. doi: 10.1002/mrm.20623.
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 Crámer-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+pik, pi/2+pik, 7pi/6+pik), 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.
水脂三点分解的噪声分析得到扩展，以考虑场图中的不确定性。这种推广导致了一个非线性估计问题。通过计算任意回波时间偏移选择下的平均信号最大有效数量（NSA），使用克拉美 - 罗界（CRB）来研究幅度、相位和场图估计的方差。分析表明，重建的幅度、相位和场图的噪声特性不仅取决于回波时间偏移的选择，还取决于每个体素中的脂肪和水的含量及其在回波时的对齐方式。使用CRB对自旋回波、扰相梯度回波和稳态自由进动成像技术的回波时间偏移选择进行了优化。幅度的噪声分析解释了在脂肪和水的边界处临床上看到的粗糙界面，其源图像是关于自旋回波对称获得的。它还通过选择适当的回波时间偏移（-π/6 + πk，π/2 + πk，7π/6 + πk）（k为整数）提供了一种解决方案。通过这种回波时间偏移的选择，可以在所有脂肪与水的比例上均匀地实现最大NSA。还对相位和场图的估计进行了优化。使用新开发的实现CRB的非线性最小二乘重建算法，通过蒙特卡罗模拟验证了这些理论结果。
