基于非精确Newton迭代正则化的EIT图像重构算法  

Study on the EIT image reconstruction algorithm based on the inexact Newton iterative regularization

作　　者：赵一帆 王静 ZHAO Yifan;WANG Jing(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2023年第2期151-159,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金(12101204,11871180,12101205)。

摘　　要：图像重构在电阻抗成像技术的实际应用中起着至关重要的作用。针对EIT图像重构问题存在的不适定性和病态性,提出了一种快速的非精确Newton迭代正则化方法,该方法包括内外两层迭代:外层迭代为非精确Newton方法且以偏差原则作为停止准则;内层迭代采用迭代正则化格式并结合选取适当的步长来加速,如Landweber迭代和同伦摄动迭代等。结果表明,与传统的迭代正则化方法相比,非精确Newton迭代正则化方法大大改进了成像效率,可达到较好的图像重构质量和鲁棒性。Image reconstruction plays a vital role in the practical application of electrical impedance tomography.To deal with the ill-posed and ill-conditional problems in the image reconstruction,a fast inexact Newton iteration regularization method is proposed.The method consists of two-layers loop iteration:the outer one is Newton iteration and the discrepancy principle is used as the stopping criterion;the inner one adopts an iterative regularization scheme with an appropriate step size for acceleration,such as Landweber iteration and homotopy perturbation iteration.The results show that,compared with the usually iterative regularization schemes,the proposed inexact Newton method significantly improves the imaging efficiency and can achieve better imaging quality and robustness.

关 键 词：电阻抗成像 图像重构 Landweber迭代 同伦摄动迭代 非精确Newton迭代 

分 类 号：O29[理学—应用数学]