CRAMER-RAO BOUNDS FOR 3-POINT DIXON IMAGING

该子项目是利用NIH/NCRR资助的中心赠款提供的资源的许多研究子项目之一。子项目和研究者（PI）可能从另一个NIH来源获得了主要资金，因此可以在其他CRISP条目中表示。所列机构为中心，不一定是研究者所在机构。引言在MRI的大多数应用中，诊断信息包含在来自组织中水的信号中。信号中的脂肪成分可能会掩盖潜在的病理。因此，抑制或分离脂肪信号是很重要的。 狄克逊成像使用在不同时间从回波获得的图像来分离每个像素中的化学物质。该技术最常见的应用是使用3次测量，即3点狄克逊成像来分离脂肪和水。3点狄克逊成像中脂肪和水的幅度估计的噪声取决于许多因素，包括回波时间、场不均匀性、脂肪-水比和重建算法1。 Cramer-Rao bound 2（CRB）是任何无偏估计方差的下界。它提供了一个测量的最小不确定性的估计，对于一个给定的数据采集，这是独立的重建算法。我们使用CRB来优化回波时间的选择，并将我们的最小二乘估计算法的性能与此理论限制进行比较。材料和方法计算CRB，以根据任意3个回波时间的测量值估计脂肪和水的大小。进行优化以找到具有最少成像时间的回波时间的选择，从而优化噪声性能。作为噪声性能的度量，我们使用平均信号数（NSA），它是原始图像方差与水估计方差的比值。在我们的情况下，NSA为3是最大可能。NSA为0表示水不能从测量中估计。为了验证理论结果，使用含有脂肪和水的球形体模进行了体外实验。通过重建相对于脂肪和水的界面的倾斜切片，我们生成具有一定范围的脂肪-水比率的像素。结论Cramer-Rao边界为狄克逊成像提供了一种计算效率高的回波时间选择优化方法。进行这样的优化以避免当像素包含相等部分的脂肪和水时NSA的损失。对于这个应用，我们已经证明了非线性最小二乘算法是有效的（因为它实现了CRB）。通过结合使用CRB来选择我们的回波时间和有效的重建算法，我们已经获得了一种成像方法，该方法在重建的水和脂肪图像的方差方面是理想的。参考资料里德等.例如，提交给MRM。2. Pineda，et.例如，提交给TMI。

This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. INTRODUCTION In most applications of MRI, the diagnostic information is contained in the signal coming from the water in tissue. The fat component of the signal can obscure underlying pathology. For this reason, it is important to suppress or separate the fat signal. Dixon imaging uses images obtained at different times from the echo to separate the chemical species in each pixel. The most common application of this technique is the separation of fat and water using 3 measurements, i.e. 3-point Dixon imaging. The noise of the estimates for the magnitude of fat and water in 3-point Dixon imaging depends on many factors including the echo times, the field inhomogeneity, the fat-to-water ratio and the reconstruction algorithm1. The Cramer-Rao bound2 (CRB) is the lower bound on the variance of any unbiased estimate. It provides a measure of the minimum uncertainty of the estimates for a given data acquisition which is independent of the reconstruction algorithm. We use the CRB to optimize the choice of echo times and compare performance of our least-squares estimation algorithm with this theoretical limit. MATERIALS AND METHODS The CRB was computed for estimating the magnitude of the fat and water from measurements at any 3 echo times. An optimization was carried out to find choice of echo times with the least imaging time that optimized the noise performance. As a measure of noise performance, we used the number of signals averaged (NSA) which is the ratio of the variance of the original images over the variance of the water estimate. In our case, an NSA of 3 is the maximum possible. An NSA of 0 says that the water cannot be estimated from the measurements. To verify the theoretical result, an in-vitro experiment was carried out using a spherical phantom containing fat and water. By reconstructing an oblique slice with respect to the interface of the fat and water, we generated pixels with a range of fat-to-water ratios. CONCLUSION Cramer-Rao bounds provide a computationally efficient way to optimize the choice of echo times for Dixon imaging. Such an optimization was carried out to avoid the loss of NSA when a pixel contained equal parts fat and water. For this application, we have shown that the non-linear least squares algorithm is efficient (since it achieves the CRB). By combining the use of the CRB to choose our echo times and a reconstruction algorithm that is efficient, we have obtained an imaging method that is ideal in terms of the variance of the reconstructed water and fat images. REFERENCES 1. Reeder, et. al., submitted to MRM. 2. Pineda, et. al., to be submitted to TMI.