Fully Bayesian Reconstructions From Single-Photon Emission Computed Tomography Data
本文提出一种完全贝叶斯方法，利用吉布斯成对差异先验和超先验，通过离线逻辑回归估计归一化常数，并用马尔可夫链蒙特卡洛方法从单光子发射计算机断层扫描数据中重建图像，提供后验均值和像素可信区间。
Abstract With suitably chosen priors, Bayesian models are useful in image reconstruction. I consider reconstructions from single-photon emission computerized tomography data using a Gibbs pairwise difference prior. A fully Bayesian approach is presented where the prior parameters are considered drawn from hyperpriors. The approach is problematical, because the normalization constant in the prior is an intractable function of its parameters. Here the constant is estimated off-line by reverse logistic regression. Markov chain Monte Carlo methods are used on simulated and real data to gain estimates of the posterior mean and pixelwise credibility bounds. The resulting reconstructions are compared to those obtained by filtered back-projection, maximum likelihood/EM, and the one-step-late solution to the fixed parameter posterior mode.