A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise

作者：Clason Christian^*; Jin Bangti

来源：SIAM Journal on Imaging Sciences, 2012, 5(2): 505-U295.

DOI：10.1137/110826187

• semismooth Newton method
• parameter identification
• impulsive noise
• L-1 data fitting
• regularization parameter
• noise model

This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L-1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented.

• 出版日期2012