Accelerated inexact Newton-Landweber iteration method for EIT image reconstruction  

EIT图像重构的加速非精确Newton-Landweber迭代法

作　　者：YANG Xue WANG Yifan WANG Jing 杨雪;王一凡;王静(黑龙江大学数学科学学院,哈尔滨150080)

机构地区：[1]School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China

出　　处：《黑龙江大学自然科学学报》2024年第6期690-699,共10页Journal of Natural Science of Heilongjiang University

基　　金：National Natural Science Foundation of China(12101204,12261021);Heilongjiang Provincial Natural Science Foundation of China(LH2023A018);Modern Numerical Method Course for Research Program on Teaching Reform of Degree and Postgraduate Education of Heilongjiang University(2024)。

摘　　要：The image reconstruction of electrical impedance tomography(EIT)is a nonlinear and ill-posed inverse problem and the imaging results are easily affected by measurement noise,which needs to be solved by using regularization methods.The iterative regularization method has become a focus of the research due to its ease of implementation.To deal with the ill-posed and ill-conditional problems in image reconstruction,the inexact Newton-Landweber iterative method is considered and the Nesterov’s acceleration strategy is introduced.One Nesterov-type accelerated version of the inexact Newton-Landweber iteration is presented to determine the conductivity distributions inside an object from electrical measurements made on the surface.In order to further optimize the acceleration,both the steepest descent step-length and the minimal error step-length are exploited during the iterative image reconstruction process.Landweber iteration and its accelerated version are also implemented for comparison.All algorithms are terminated by the discrepancy principle.Finally,the performance is tested by reporting numerical simulations to verify the remarkable acceleration efficiency of the proposed method.电阻抗层析成像(Electrical impedance tomography,EIT)图像重构问题属于非线性不适定逆问题,其成像结果很容易受到测量噪声的影响,需要使用正则化方法对其进行求解。迭代正则化方法因其易于实现的优势成为研究的重点。针对EIT图像重构问题存在的不适定性和病态性,考虑非精确Newton-Landweber迭代法,并引入Nesterov加速策略,提出了一种非精确Newton-Landweber迭代法的Nesterov加速版本,用于根据物体表面的电学测量结果来确定物体内部的电导率分布情况。为进一步优化加速效果,在迭代图像重构过程中分别测试了最速下降步长和最小误差步长。为便于比较,还测试了Landweber迭代及其加速版本,所有算法均采用偏差原则作为终止准则,通过数值模拟验证了所提方法的有效性及加速效率。

关 键 词：electrical impedance tomography image reconstruction Landweber iteration inexact Newton-Landweber iteration Nesterov acceleration 

分 类 号：O241.6[理学—计算数学]