基于最优权重的三维非局部均值图像去噪算法  

The Optimal Weights of Non-local Means for 3D Image Denoising

作　　者：赵元 李真 金其余[1] ZHAO Yuan;LI Zhen;JIN Qiyu(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;School of Mathematics and Statistics,Guangdong University of Finance&Economics,Guangzhou 510320,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]广东财经大学统计与数学学院,广州510320

出　　处：《内蒙古大学学报（自然科学版）》2023年第2期113-120,共8页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金(12061052);内蒙古大学研究生创新创业专项经费(11200-121024);内蒙古自治区“高校青年科技英才”(NJYT22090);内蒙古自治区高等学校创新团队发展计划支持(NMGIRT2207);广东省教育科学规划项目(高等教育科学研究专项)(2021GXJK201)。

摘　　要：将二维非局部均值的优化理论和收敛性定理推广到三维情形,并提出了具有最优权重的三维非局部均值算法。首先通过最小化L2估计的上界,得出了三维非局部均值算法的自适应平滑参数的最优加权。接着证明提出的算法在统计上是以最优速度收敛的。仿真实验表明,与其它去噪方法相比,本文算法能够有效去除各类方差稳定的独立同分布随机噪声,并且具有更好的估计结果。The optimization theories and convergence theorems of 2-dimensional non-local means are extended to 3-dimensional(3D),and a 3D non-local means algorithm with optimal weights is proposed.Firstly,the optimal weights with the adaptive smoothing parameters of the 3D non-local means is obtained by minimizing the upper bound of the L_2 estimation.Then it is proved that the proposed method converges statistically at the optimal rate.Simulation results show that the proposed algorithm significantly removes all types of independent and identically distributed variance-stabilized noise,and has better results.

关 键 词：非局部均值 独立同分布 最优权重 图像去噪 

分 类 号：O224[理学—运筹学与控制论]