Semismooth Newton method for minimization of the LLT model

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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

Abstract
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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.

Keywords: image denoising, LLT model, Semismooth Newton method, global convergence., Q-superlinear convergence.

Mathematics Subject Classification: Primary: 65K10, 94A8; Secondary: 90C3.

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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