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Abstract：
Q-space trajectory imaging (QTI) enables the estimation of useful scalar measures indicative of the local tissue structure. This is accomplished by employing generalized gradient waveforms for diffusion sensitization alongside a diffusion tensor distribution (DTD) model. The first two moments of the underlying DTD are made available by acquisitions at low diffusion sensitivity (b-values). Here, we show that three independent conditions have to be fulfilled by the mean and covariance tensors associated with distributions of symmetric positive semidefinite tensors. We introduce an estimation framework utilizing semi-definite programming (SDP) to guarantee that these conditions are met. Applying the framework on simulated signal profiles for diffusion tensors distributed according to non-central Wishart distributions demonstrates the improved noise resilience of QTI+ over the commonly employed estimation methods. Our findings on a human brain data set also reveal pronounced improvements, especially so for acquisition protocols featuring few number of volumes. Our method\'s robustness to noise is expected to not only improve the accuracy of the estimates, but also enable a meaningful interpretation of contrast in the derived scalar maps. The technique\'s performance on shorter acquisitions could make it feasible in routine clinical practice.
摘要：
Q空间轨迹成像(QTI)使得能够估计指示局部组织结构的有用标量测量。这是通过与扩散张量分布（DTD）模型一起使用广义梯度波形进行扩散敏化来实现的。通过在低扩散灵敏度（b值）下的采集，可以获得基础DTD的前两个矩。这里,我们证明了与对称正半定张量分布相关的均值和协方差张量必须满足三个独立条件。我们引入了一种利用半定编程（SDP）的估计框架，以确保满足这些条件。将框架应用于根据非中心Wishart分布分布的扩散张量的仿真信号轮廓上，证明了与常用的估计方法相比，QTI的抗噪能力得到了改善。我们对人脑数据集的发现也揭示了显着的改善，尤其是对于具有少量卷的采集协议。我们的方法对噪声的鲁棒性有望不仅提高估计的准确性，而且还可以对导出的标量图中的对比度进行有意义的解释。该技术在较短的采集上的性能可以使其在常规临床实践中可行。
