基于分段常值水平集的抛物型方程的参数识别算法

A New Algorithm Scheme for Parameter Identification Based on Piecewise Constant Level Set Method

研究了线性抛物型方程不连续参数的识别算法.根据原有算法对于加噪观测数据计算不收敛的问题,本文基于分段常值水平集方法,根据水平集函数和优化过程的特点,修正原有Uzawa型算法中的带有总变差(TV)正则化的极小化模型和对常值向量的极小化模型,并且利用分裂Bregman迭代算法处理TV范数的优越性,构造一种新的参数识别算法格式.数值实验结果显示,新算法具有计算时间短、精度高、抗噪性强的优点.

A piecewise constant level set method was applied to parabolic inverse problem with discontinuous parameter. According to the feature of level set function and optimization process, combined with split Bregman method which has the advantage of handing the total variation norm, the existing minimization functions in Uzawa algorithm and original algorithm scheme was modified. And then a new algorithm scheme was given. Numerical experiments show that the new algorithm has advantages of short computing time, high precision and strong performance of anti - noise.