基于非凸非光滑变分模型的灰度图像泊松噪声移除算法  

Nonconvex nonsmooth variational model for Poisson noise removal of gray image

作　　者：张远鹏 陈鸿韬 王伟娜 ZHANG Yuanpeng;CHEN Hongtao;WANG Weina(School of Sciences,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《浙江大学学报（理学版）》2023年第2期160-166,173,共8页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(12001144);浙江省自然科学基金资助项目(LQ20A01007).

摘　　要：基于非凸变分方法在图像边界结构保持和对比度保持上的优势,针对泊松噪声的移除问题提出一种新的非凸非光滑正则化模型及快速求解算法。模型由非凸Lipschitz势函数复合图像梯度信息的正则化项和非线性Kullback-Leibler数据保真项两部分构成。通过使用临近点线性化策略,将求解非凸变分模型转化为求解一系列凸变分模型,进而使用交替方向乘子法求解。同时证明了算法的目标函数值序列具有单调下降性。实验结果表明,该方法能有效消除图像中的泊松噪声,且信噪比较经典算法有明显提升。Based on the advantages of nonconvex variational models on image edge-preserving and contrast-preserving,this paper introduces a new nonconvex and nonsmooth variational model together with a fast algorithm for the Poisson noise removal.The proposed model consists of a regularization term and a data fidelity term.The regularization term is formulated by a nonconvex Lipschitz potential function composed of the first-order derivative of images,while the data fitting term is depicted by the nonlinear Kullback-Leibler divergence.By using the proximal linearization strategy,the proposed nonconvex and nonsmooth model can be converted into a series of convex models,which are able to be solved by alternating direction method of multipliers.Moreover,we can also prove the monotonic decreasing property of the objective function value sequence.Numerical experiments show that our model with the proposed algorithm is effective for eliminating Poisson noise and obtains higher SNR values compared to classical methods.

关 键 词：泊松噪声移除 非凸非光滑 临近点线性化 交替方向乘子法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]