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H. Jiang, D. Ralph. Global and local superlinear con-vergence analysis of Newton-type methods for semismooth equations with smooth least squares, in Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi (eds.), Kluwer Acad. Publ., Dordrecht, 1998:181-209.

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• 标题: 基于ROF模型的修正半光滑牛顿法The Modified Semismooth Newton Algorithm Based on the ROF Model

  作者: 庞志峰, 吕军成

  关键字: 图像去噪, 全变差, 半光滑牛顿法: Image Denoising; Total Variation; Semismooth Newton Algorithm

  期刊名称: 《Pure Mathematics》, Vol.1 No.1, 2011-04-15

  摘要: 本文基于ROF去噪模型的对偶算法提出一个修正的半光滑牛顿法。文中证明了该算法具有Q超线性收敛，同时指出选取适当的参数α可以提高数值计算效率。实验表明，建议的修正算法既能较好的复原图像，又具有较快的收敛速度。 In this paper, based on the dual algorithm of ROF model, we propose a modified semismooth Newton algorithm. Furthermore, we prove that the proposed algorithm converges Q-superlinearly, and also refer that this algorithm can improve the computational efficiency by choosing a suitable parameter α. The simulations show that the new modified algorithm can perfectly restore image and keep the faster conver-gence rate.