基于贝叶斯理论快速ERT图像重建算法

Fast image reconstruction algorithm based on Bayesian estimation theory for electrical resistance tomography

针对电阻层析成像系统中图像重建不适定问题,与现有ERT图像代数重建算法不同,提出一种基于贝叶斯理论快速一步动态图像重建算法。在阐述电阻层析成像的理论基础上,利用有限元方法建立敏感场数学模型,得到灵敏度矩阵和投影数据。在分析贝叶斯理论基础上,推导出快速一步动态图像重建模型,并将介质分布的先验信息和噪声随机信息等统计信息引入到图像重建中,实现对电导率的重建。分析了不同分布先验概率参数和不同噪声信噪比等影响因子对算法重建结果的影响,并与高斯牛顿迭代、贝叶斯迭代重建算法相比较。结果表明,所提算法重建速度有很大提高,并能较好反映被测介质的相对位置。

To solve the ill-posed problem in electrical resistance tomography （ERT） technology, this paper proposed a one-step dynamic image reconstruction algorithm based on Bayesian theorem ,it which was different to the existing ERT image reconstruction algorithms. Based on the basic theory of resistance tomography, it solved the sensitive field mathematical model by finite element method to obtain the sensitivity matrix and project data. Next, based on analysis of Bayesian theorem, it derived one-step dynamic reconstruction algorithm model. And it was taken into account statistical information including the prior probability of permittivity distribution and the noise information which was applied for image reconstruction. Finally, it researched the function of impact fac- tors including the prior probability parameters and different signal-to-noise ratio（SNR） to reconstructed result under different dis- tribution. Meanwhile, the presented method was compared with Gauss-Newton iteration and Bayesian iteration methods. The results show that this algorithm gets better effect in the precision and speed than others iteration methods.