基于两步正则化Gauss-Newton迭代算法的ECT图像重建

An Image Reconstruction Method of ECT Based on Two-step Regularization Gauss-NewtonIterative Algorithm

电容层析成像(ECT)技术求解图像重建问题属于非线性问题,并且存在严重的不适定性。为提高图像重建精度,提出了一种基于两步正则化Gauss-Newton迭代算法的ECT图像重建方法。针对标准正则化Gauss-Newton迭代算法在图像重建中存在的不收敛问题,引入了两步迭代方法;改进了正则化矩阵,提高了解估计的精确度;考虑到Gauss-Newton算法对迭代初值的依赖性,加入了同伦算法。最后,进行仿真和静态实验,并与线性反投影(LBP)算法、Landweber算法、Tikhonov正则化算法进行对比。结果表明,该方法可有效提高图像重建精度。

Electrical capacitance tomography(ECT)is a nonlinear problem and has serious ill-posed.In order to improve the accuracy of image reconstruction,an ECT image reconstruction method based on two-step regularized Gauss-Newton iterative algorithm is proposed.Aiming at the non-convergence problem of standard regularized Gauss-Newton iterative algorithm in image reconstruction,a two-step iterative method is introduced.The regularization matrix is improved,which improves the accuracy of estimation.Considering the dependence of Gauss-Newton algorithm on the initial value of iteration,homotopy algorithm is added.Finally,the simulation and static experiment are carried out,and compared with the linear back projection(LBP)algorithm,Landweber algorithm and Tikhonov regularization algorithm,the results show that this method can effectively improve the accuracy of image reconstruction.