Qi J, Leahy R M
Signal and Image Processing Institute, University of Southern California, Los Angeles 90089-2564, USA.
IEEE Trans Med Imaging. 2000 May;19(5):493-506. doi: 10.1109/42.870259.
We derive approximate analytical expressions for the local impulse response and covariance of images reconstructed from fully three-dimensional (3-D) positron emission tomography (PET) data using maximum a posteriori (MAP) estimation. These expressions explicitly account for the spatially variant detector response and sensitivity of a 3-D tomograph. The resulting spatially variant impulse response and covariance are computed using 3-D Fourier transforms. A truncated Gaussian distribution is used to account for the effect on the variance of the nonnegativity constraint used in MAP reconstruction. Using Monte Carlo simulations and phantom data from the microPET small animal scanner, we show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of MAP reconstruction for priors with quadratic energy functions. We also describe how these analytical results can be used to achieve near-uniform contrast recovery throughout the reconstructed volume.
我们推导了使用最大后验（MAP）估计从全三维（3-D）正电子发射断层扫描（PET）数据重建图像的局部脉冲响应和协方差的近似解析表达式。这些表达式明确考虑了三维断层扫描仪的空间变化探测器响应和灵敏度。所得的空间变化脉冲响应和协方差使用三维傅里叶变换进行计算。截断高斯分布用于考虑MAP重建中使用的非负性约束对方差的影响。使用来自microPET小动物扫描仪的蒙特卡罗模拟和体模数据，我们表明，对于具有二次能量函数的先验，这些近似为MAP重建的对比度恢复和协方差提供了相当准确的估计。我们还描述了如何利用这些分析结果在整个重建体积中实现近乎均匀的对比度恢复。
