各向异性的L_(0)正则化图像平滑方法  

An anisotropic L_(0)regularized image smoothing method

作　　者：赵吴帆 武文娜 武婷婷[1] ZHAO Wufan;WU Wenna;WU Tingting(College of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学理学院,江苏南京210023

出　　处：《南京邮电大学学报（自然科学版）》2024年第4期131-138,共8页Journal of Nanjing University of Posts and Telecommunications：Natural Science Edition

基　　金：国家自然科学基金(61971234,12126340,12126304,11501301);江苏省研究生科研与实践创新计划项目(KYCX23_0958)资助项目。

摘　　要：现有的图像平滑方法缺乏灵活性,会导致边缘不清晰、结构缺失和过度锐化等问题。文中提出一种新的自适应加权矩阵的正则化方法,主要应用于图像平滑,并且可以扩展到其他应用。提出的模型设计了一个新的正则化项,基于梯度算子▽和自适应加权矩阵T组合为L_(0)范数正则化项,使得模型具有各向异性。通过为不同梯度方向赋予不同的权重,以此来刻画平滑图像的局部结构,更好地展现局部特征,防止过度平滑。由于所提出的模型是非光滑且非凸的,在求解上比较复杂,因此采用ADMM算法对模型进行求解。把目标函数分解成几个易求解的子问题,分别对每个子问题求解,最终得到模型的最优解。主客观实验表明,提出的模型在视觉效果以及数值方面都有明显的提高。Existing image smoothing methods usually lack flexibility and cause problems,such as unclear edges,missing structures,and excessive sharpening.To tackle these problems,this paper proposes a novel regularization method involving an adaptive weighted matrix.This method is primarily applied to image smoothing and can be extended to other applications.It introduces a new regularization term by combining gradient operators▽and an adaptive weighted matrix T into a L_(0)norm regularization term,and imparting anisotropic characteristics to the model.Through assigning different weights to various gradient directions,the model characterizes the local structure of smoothed images,thus local features can be better emphasized and excessive smoothing can be prevented.Given that the proposed model is non-smooth and non-convex,solving it is relatively complex.Thus,the ADMM algorithm is employed to solve the model by decomposing the objective function into several easily solvable subproblems.Each subproblem is solved separately,and the optimal solution for the model is ultimately obtained.Both subjective and objective experiments indicate a significant improvement in both visual effects and numerical aspects by the proposed model.

关 键 词：图像平滑 L_(0)正则化 自适应加权矩阵 各向异性 交替方向乘子法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]