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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.

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
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