Stayman J Webster, Fessler Jeffrey A
Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, MI 48109-2122, USA.
IEEE Trans Med Imaging. 2004 Dec;23(12):1543-56. doi: 10.1109/TMI.2004.837790.
Resolution and covariance predictors have been derived previously for penalized-likelihood estimators. These predictors can provide accurate approximations to the local resolution properties and covariance functions for tomographic systems given a good estimate of the mean measurements. Although these predictors may be evaluated iteratively, circulant approximations are often made for practical computation times. However, when numerous evaluations are made repeatedly (as in penalty design or calculation of variance images), these predictors still require large amounts of computing time. In Stayman and Fessler (2000), we discussed methods for precomputing a large portion of the predictor for shift-invariant system geometries. In this paper, we generalize the efficient procedure discussed in Stayman and Fessler (2000) to shift-variant single photon emission computed tomography (SPECT) systems. This generalization relies on a new attenuation approximation and several observations on the symmetries in SPECT systems. These new general procedures apply to both two-dimensional and fully three-dimensional (3-D) SPECT models, that may be either precomputed and stored, or written in procedural form. We demonstrate the high accuracy of the predictions based on these methods using a simulated anthropomorphic phantom and fully 3-D SPECT system. The evaluation of these predictors requires significantly less computation time than traditional prediction techniques, once the system geometry specific precomputations have been made.
分辨率和协方差预测器先前已针对惩罚似然估计器推导得出。给定均值测量的良好估计值，这些预测器可以为断层扫描系统的局部分辨率特性和协方差函数提供准确的近似值。尽管这些预测器可以迭代评估，但为了实际计算时间，通常会采用循环近似。然而，当重复进行大量评估时（如在惩罚设计或方差图像计算中），这些预测器仍然需要大量的计算时间。在Stayman和Fessler（2000年）的研究中，我们讨论了针对平移不变系统几何形状预先计算大部分预测器的方法。在本文中，我们将Stayman和Fessler（2000年）中讨论的有效程序推广到平移可变单光子发射计算机断层扫描（SPECT）系统。这种推广依赖于一种新的衰减近似以及对SPECT系统对称性的若干观察结果。这些新的通用程序适用于二维和全三维（3-D）SPECT模型，既可以预先计算并存储，也可以写成程序形式。我们使用模拟的人体模型和全三维SPECT系统，证明了基于这些方法的预测具有很高的准确性。一旦进行了系统几何形状特定的预先计算，这些预测器的评估所需的计算时间比传统预测技术要少得多。
