电磁层析成像技术中的谱参数混合共轭梯度法

Spectral parameters hy brid conj ugate gradient method in electromagnetic tomography technology

电磁层析成像技术是基于电磁感应原理的过程检测技术,图像重建是解决其反问题的关键.基于共轭梯度算法,修正搜索方向和迭代参数,推导出基于谱参数的混合共轭梯度算法,以提高图像重建质量和收敛性.介绍了电磁层析成像系统的实验室模型和灵敏度分布矩阵,作为反问题基础;对搜索方向进行修正,提出一个新的谱参数,用来控制新旧搜索方向之间的角度,根据每一步迭代的残差结果,寻找最优解;改善共轭参数,分析非线性共轭梯度算法中FR算法(fletcher-reeves method)和PRP算法(polak-ribiere-polyak method)的各自优势,将它们按照一定比例进行混合,得到一种新的混合共轭梯度算法;将谱参数混合共轭梯算法应用到电磁层析成像实验室系统中,构建了3种典型实验室模型,对比谱参数混合共轭梯度算法与传统算法并作出评价.实验结果表明:谱参数混合共轭梯度算法的重建图像的质量更高,具有较好的数值表现;混合共轭梯度算法结合了FR算法和PRP算法的优点,收敛速度比PRP算法快,成像质量比其他算法高.

Electromagnetic tomography is a kind of process detection technology based on the principle of electromagnetic induction.Image reconstruction is the key to solve its inverse problem.Based on the conjugate gradient algorithm,the search direction and iteration parameters are modified.A hybrid conjugate gradient algorithm based on spectral parameters is derived to improve the quality and convergence of image reconstruction.The laboratory model and sensitivity distribution matrix of the electromagnetic tomography technology system are introduced as the basis of the inverse problem.A new spectral parameter conjugate gradient algorithm is proposed to modify the search direction,which is used to control the angle between the old and new search directions.The search direction is determined according to the residual of each step in order to find the optimal solution.Combining the advantages of FR algorithm and PRP algorithm in nonlinear conjugate gradient algorithm,they are mixed by certain proportion to obtain a new hybrid conjugate gradient algorithm.The spectral parameter hybrid conjugate gradient method is applied to the electromagnetic tomography technology laboratory system,three typical la boratory models are constructed,and the spectral parameter hybrid conjugate gradient algorithm and the traditional algorithm are compared and evaluated.The experimental results show that the spectral parameter hybrid conjugate gradient algorithm has higher quality of reconstructed image and better numerical performance,and it combines the advantages of FR algorithm and PRP algorithm,with faster convergence speed and higher imaging quality than other algorithms.