摘要
本文对图像去噪的ROF模型的非线性项▽·((▽u)/((|▽u|2+β)1/2)构造了几个新的差分格式.用不动点迭代法求解得到的非线性系统,并在每一步的迭代中用代数多重网格法求解对应的大型稀疏线性方程组.最后对不同的含有高斯白噪声的图像进行了处理,结果表明本文的算法是有效的和可靠的.
In this paper,several difference schemes to the highly nonlinear term▽·((▽u)/((|▽u|2+β)1/2)of the total variation-based image denoising problem are proposed.The large nonlinear system is linearized by fixed point iteration method.An algebraic multigrid method with Krylov subspace acceleration is used to solve the corresponding linear equations.Different pictures with Gaussian white noise are processed in the numerical experiments.The numerical experiments demonstrate that our difference schemes are efficient and robust.
作者
许秋滨
XU QIUBIN(School of stαtisticsα叽d mαthemαtics,N,α叩呵Audit Univer肘:ty,Nαnji叽g 211815,China)
出处
《应用数学学报》
CSCD
北大核心
2019年第4期470-481,共12页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(61673221)
国家自然科学基金(11701287)
江苏省高校自然科学基金(12KJB110008)资助项目
关键词
差分格式
图像去噪
不动点迭代
代数多重网格法
difference scheme
image denoising
total variation
fixed point method
algebraic multigrid method
Krylov acceleration
