# zbMATH — the first resource for mathematics

Semismooth Newton method for minimization of the LLT model. (English) Zbl 1186.65082
Summary: We discuss the nonsmooth second-order regularization, suggested by M. Lysaker, A. Lundervold and X. Tai (LTT) [IEEE Trans. Image Process 12, 1579–1590 (2003)], 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.

##### MSC:
 65K10 Numerical optimization and variational techniques 49J20 Existence theories for optimal control problems involving partial differential equations 49M15 Newton-type methods 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
Full Text: