基于贝叶斯分层模型的MCMC方法在闪光图像重建中的应用

Applications of MCMC method based on Bayesian hierarchical model in flash radiography reconstruction

针对闪光图像得到的光程数据,采用贝叶斯分层模型建立了后验概率模型,运用Gibbs抽样动态构造马尔可夫链;进而获得了关于线吸收系数的统计结果及其不确定度,并与约束共轭梯度(CCG)方法进行对比分析。数值实验结果表明,马尔可夫链蒙特卡罗(MCMC)方法对理想光程图像的重建结果与真值近似完全一致;在含模糊和噪声时,重建结果与CCG方法相当;当含模糊且噪声干扰较大时,MCMC方法的重建结果要略优于CCG;更重要的是MCMC方法能够给出重建结果的不确定度。

The Markov chain Monte Carlo（MCMC） method combined with Bayesian theory can not only use prior information flexibly, but also give the uncertainty of solution. There is a bright application prospect in quantitative diagnosis of flash radiography. For the optical path length data of the flash radiographic images, a posterior probability model is built by Bayesian hierarchical model, and the Markov chain is dynamically constructed by Gibbs sampling. Then the statistical results of linear attenuation coefficients and their uncertainty are obtained and compared with the constrained conjugate gradient （CCG） method. The results of numerical experiments show that the reconstruction result of MCMC method is approximately the same as the true data for the ideal FTO optical path length image. In the case of blurring and noise, the reconstructed result is equivalent to that by the CCG method. Even when the blurred optical path length data is interfered by high noise, the result of MCMC is slightly better than that of CCG. More importantly, the uncertainty of the reconstruction can be provided by MCMC method. The related work in this paper verifies the feasibility of MCMC reconstruction of flash radiographic images and lays a good foundation for MCMC reconstruction with blurred and noised transmissivity images.