Uncertainties of calculated Cramer-Rao lower bounds: implications for quantitative MRS
Uncertainties of calculated Cramer-Rao lower bounds: implications for quantitative MRS
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DOI：
10.1002/mrm.27415
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发表时间：
2019-02-01
影响因子：
3.3
通讯作者：
Pages, Guilhem
中科院分区：
文献类型：
--
作者：
Bonny, Jean-Marie;Pages, Guilhem
目的：研究相对Cramer-Rao下限(RCRB)估计的不确定度，并论证其在MRS定量中的偏差效应。理论和方法：模拟计算几种rCRB水平下的rCRB的分布。对包含1个信号(单重态)或2个部分重叠信号的模拟核磁共振信号进行每rCRB值10万次模拟。为不同的阈值水平编制假阳性和假阴性风险。结果：(1)rCRB*分布是不对称的，右尾分布增加了接受假阳性数据的风险(即接受rCRB*值，而真rCRB值高于阈值水平)；(2)分布宽度随着rCRB水平的增加而增加。具有重叠峰值的模拟会导致rCRB估计的更不准确。错误检测的概率随着阈值水平的增加而增加。结论：基于实验测量的CRB(或rCRB)分析结果可能会导致误解。为了利用rCRB*作为拒绝标准，建议使用20%的保守阈值水平，以限制错误警报的概率。
Purpose: To investigate the uncertainties on relative Cramer-Rao lower bound (rCRB) estimates and demonstrate their biasing effects in MRS quantification.Theory and Methods: Simulations were performed to calculate the distribution of the computed rCRB (noted rCRB*) for several rCRB levels. One hundred thousand simulations per rCRB value were performed on simulated NMR signals containing either 1 signal (singlet) or 2 partially overlapping signals. False-positive and false-negative risks were compiled for different threshold levels. rCRB* distribution was experimentally checked on a deuterated water sample using a 9.4 Tesla vertical magnet.Results: Simulations showed that (1) rCRB* distribution is asymmetrical, with a right-tailed distribution increasing the risk of accepting false-positive data (i.e., accepting an rCRB* value whereas the true rCRB value is higher than the threshold level) and (2) distribution broadness increases with increasing rCRB level. Simulations with overlapped peaks lead to more inaccuracy in the rCRB estimation. Probabilities of false detection increase with increasing threshold level.Conclusion: Analyzing results thanks to a CRB (or rCRB) based on experimental measurements might lead to misinterpretations. To exploit the rCRB* as rejection criteria, a conservative threshold level of 20% is recommended in order to limit the probability of false alarms.