Dept. of Radiol., Pennsylvania Univ., Philadelphia, PA.
IEEE Trans Med Imaging. 1991;10(3):336-46. doi: 10.1109/42.97583.
An image reconstruction method motivated by positron emission tomography (PET) is discussed. The measurements tend to be noisy and so the reconstruction method should incorporate the statistical nature of the noise. The authors set up a discrete model to represent the physical situation and arrive at a nonlinear maximum a posteriori probability (MAP) formulation of the problem. An iterative approach which requires the solution of simple quadratic equations is proposed. The authors also present a methodology which allows them to experimentally optimize an image reconstruction method for a specific medical task and to evaluate the relative efficacy of two reconstruction methods for a particular task in a manner which meets the high standards set by the methodology of statistical hypothesis testing. The new MAP algorithm is compared to a method which maximizes likelihood and with two variants of the filtered backprojection method.
讨论了一种基于正电子发射断层扫描（PET）的图像重建方法。由于测量往往存在噪声，因此重建方法应该包含噪声的统计特性。作者建立了一个离散模型来表示物理情况，并得到了问题的非线性最大后验概率（MAP）公式。提出了一种需要求解简单二次方程的迭代方法。作者还提出了一种方法，允许他们针对特定的医学任务对图像重建方法进行实验优化，并以满足统计假设检验方法设定的高标准的方式评估两种特定任务的重建方法的相对效果。将新的 MAP 算法与最大化似然的方法以及两种滤波反投影方法的变体进行了比较。
