摘要
针对马尔可夫链蒙特卡罗(MCMC)算法的计算量大以及统计结果中含有严重噪声等问题,提出一种基于分层模型和低秩近似的X射线图像重建方法。首先引入全变差(TV)正则项来构造目标函数,并基于Jeffreys先验定义超参数以建立分层贝叶斯模型。然后采用变量分裂法得到分裂形式下各变量的条件概率密度分布。最后根据正向模型所具有的低秩性质来计算低秩近似的目标分布函数,从而得到关于待求参数的闭合解。结果表明,所提方法可以有效解决贝叶斯逆问题中存在的计算量大等问题。相比于现有的基于不确定性量化重建方法,所提方法在有效抑制图像噪声的同时能够更好地保留图像的边缘细节。
In view of the large amount of calculation of Markov Chain Monte Carlo(MCMC)algorithm and the serious noise in the statistical results,an X-ray image reconstruction method based on a hierarchical model and low-rank approximation is proposed.First,a total variation(TV)regular term is introduced to construct the objective function,and hyperparameters are defined based on Jeffreys prior to establish a hierarchical Bayesian model.Then,the variable split method is used to obtain the conditional probability density distribution of each variable in the split form.Finally,according to the low-rank nature of the forward model,the objective distribution function of the low-rank approximation is calculated,so as to obtain the closed solution of the parameters to be sought.The results show that the proposed method can effectively solve the large amount of calculation in the Bayesian inverse problem.Compared with the existing reconstruction methods based on uncertainty quantification,the proposed method can effectively suppress the image noise while retaining the edge details of the image better.
作者
王佳妤
许金鑫
李庆武
Wang Jiayu;Xu Jinxin;Li Qingwu(College of Internet of Things Engineering,Hohai University,Changzhou,Jiangsu 213022,China)
出处
《激光与光电子学进展》
CSCD
北大核心
2021年第6期132-139,共8页
Laser & Optoelectronics Progress
基金
国家自然科学基金(U1830105)。
