不连续介质反演的原对偶牛顿法和全变差正则化

摘要

研究利用散射场测量数据反演非均匀介质的逆散射问题,特别是平面波在非均匀介质中传播时所产生逆散射问题的数值计算.为克服非均匀介质不连续变化和反演具有不适定性的困难,提出基于全变差正则化的原对偶牛顿方法,避免了一般正则化方法对不连续介质交界处反演的过光滑性作用.数值试验显示,本算法可以在观测数据带有一定噪声的境况下有效地重构不连续介质系数.%An inverse scattering problem of inhomogeneous mediums from the measurements of the scattered field is considered.In particular,it focuses on the numerical computation of the inverse scattering generated by the interaction of a plane wave and an inhomogeneous medium.To solve the ill-posedness as well as the difficulties caused by inhomogeneous media,a primal-dual Newton method based on the total variation regularization is constructed.The overly smooth effect of the usual regularization method for the inversion is overcome.Numerical experiments show that this method can recover discontinuous coefficients under moderate amount of noise in the observation data.