# American Institute of Mathematical Sciences

November  2009, 3(4): 677-691. doi: 10.3934/ipi.2009.3.677

## Semismooth Newton method for minimization of the LLT model

 1 College of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan, China, China

Received  March 2009 Revised  May 2009 Published  October 2009

In this paper, we discuss the nonsmooth second-order regularization, suggested by Lysaker, Lundervold and Tai, and its application in image denoising. A function space $BV^2$ is given and the well-posedness of the LLT model is proved in this function space. By means of the Fisher-Burmeister NCP function, we reformulate the dual formula of the LLT model in discrete setting as a system of semismooth equations. Then we propose a semismooth Newton method for the LLT model to build up a Q-superlinearly convergent numerical scheme. The computational experiments are supplied to demonstrate the efficiency of the proposed method.
Citation: Zhi-Feng Pang, Yu-Fei Yang. Semismooth Newton method for minimization of the LLT model. Inverse Problems & Imaging, 2009, 3 (4) : 677-691. doi: 10.3934/ipi.2009.3.677
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