正则化-同伦方法用于电阻抗断层成像(英文)

Tikhonov regularization-homotopy method for electrical impedance tomography

电阻抗断层成像问题本质上是一个非线性、不适定反问题,必须进行正则化处理。基于Tik-honov正则化方法,结合大范围收敛的同伦方法,设计Tikhonov正则化-同伦方法,旨在克服传统重构算法(如Newton类算法等)的局部收敛性,解决初值难以有效选取的难题。针对电阻抗断层成像的图像重建仿真试验,结果表明该方法的有效性与全局收敛性。

The solution of impedance distribution in electrical impedance tomography（EIT） is a nonlinear inverse problem that requires to the use of a regularization method.The Tikhonov regularization methods have been popular in the solution of many inverse problems.Traditional reconstruction algorithms like Newton method and Newton-like methods which were effected by the presence of local minima of the objective function may diverge if a good initial estimate cannot be provided,it is important to loosen the limits of initial values of iterative algorithm.Therefore,widely convergent homotopy method to solve the minimization problem of the objective function is used.A new approach named Tikhonov regularization-homotopy method for EIT image reconstruction is proposed.A synthetic example demonstrates that our method is more likely to find a global minimum than normal iterative methods.