Hermansen F, Bloomfield P M, Ashburner J, Camici P G, Lammertsma A A
Cyclotron Unit, MRC Clinical Sciences Centre, Royal Postgraduate Medical School, Hammersmith Hospital, London, UK.
Phys Med Biol. 1995 Nov;40(11):1921-41. doi: 10.1088/0031-9155/40/11/011.
Using unitary transformations together with a previously described statistical theory for optimal linear dimension reduction it is shown how pixels in a sequence of images can be decomposed into a sum of variates, covariates, and residual vectors, with all covariances equal to zero. It is demonstrated that this decomposition is optimal with respect to noise. In addition, it results in simplified and well conditioned equations for dimension reduction and elimination of covariates. The factor images are not degraded by subdivision of the time intervals. In contrast to traditional factor analysis, the factors can be measured directly or calculated based on physiological models. This procedure not only solves the rotation problem associated with factor analysis, but also eliminates the need for calculation of the principal components altogether. Examples are given of factor images of the heart, generated from a dynamic study using oxygen-15-labelled water and positron emission tomography. As a special application of the method, it is shown that the factor images may reveal any contamination of the blood curve derived from the original dynamic images with myocardial activity.
结合酉变换以及先前描述的用于最优线性降维的统计理论，展示了如何将图像序列中的像素分解为变量、协变量和残差向量之和，且所有协方差均为零。结果表明，这种分解在噪声方面是最优的。此外，它还能得到用于降维和消除协变量的简化且条件良好的方程。因子图像不会因时间间隔的细分而退化。与传统因子分析不同，因子可以直接测量或基于生理模型计算。该过程不仅解决了与因子分析相关的旋转问题，还完全消除了计算主成分的需求。给出了使用氧 - 15标记水和正电子发射断层扫描进行动态研究生成的心脏因子图像示例。作为该方法的一个特殊应用，结果表明因子图像可以揭示从原始动态图像导出的血液曲线中是否存在心肌活动的任何干扰。
