基于MCMC方法的电容成像图像重构算法

Markov chain Monte Carlo (MCMC) based image reconstruction algorithm for electrical capacitance tomography

研究基于概率统计的电容成像图像重构算法,以马尔科夫随机场的方式给出介电常数分布的先验概率,利用电容成像(electrical capacitance tomography,ECT)线性模型得到似然函数,通过马尔科夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)方法对介电常数分布的后验概率密度进行采样,马尔科夫链的转移核利用Metropolis-Hastings方法得到,结合嵌套迭代提高计算效率。仿真结果表明,嵌套迭代-MCMC方法在正则化参数设置合适的条件下,可以得到较好的图像质量,基于MCMC方法图像重构算法为解决ECT图像重构问题提供一种新思路。

An image reconstruction algorithm based on statistical model for electrical capacitance tomography（ECT） is proposed.The prior probability and likelihood function are obtained using multi-level Markov random field and ECT liner model.Using MCMC sampling,the posterior distribution of permittivity is estimated.Meanwhile,nested iteration is introduced to improve the calculation efficiency.Simulation results show that the nested iteration-MCMC can enhance the calculation speed significantly and provide reconstruction images with higher quality if a proper regularization parameter is used.The MCMC based method provides a new way for ECT image reconstruction.