双加权Schatten-p范数最小化彩色图像去噪  

Double weighted Schatten-p norm minimization for real color image denoising

作　　者：姜伟[1] 杨天旭 张长胜[2] JIANG Wei;YANG Tianxu;ZHANG Changsheng(School of Mathematics, Liaoning Normal University, Dalian 116029, China;College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou 325035, China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029 [2]温州大学计算机与人工智能学院,浙江温州325035

出　　处：《辽宁师范大学学报（自然科学版）》2020年第4期433-440,共8页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61771229)。

摘　　要：相对于灰度图像去噪,彩色图像去噪更难,这是当今研究热点之一.针对彩色图像去噪问题,提出了一种双加权Schatten-p范数最小化的彩色图像去噪算法.该方法首先对R,G,B 3个通道分别进行分块,并将分块矩阵连接起来以利用通道冗余,然后根据各个通道内不同的噪声统计量引入加权矩阵,用来平衡数据保真度.利用加权Schatten-p范数作为低秩惩罚项,构建一个带有等式约束的优化问题,利用交替乘子方向法进行求解,每个迭代更新步骤都存在闭式解,确保最终结果的收敛性.实验结果表明,与最新去噪算法对比,所提出的算法在相同条件下具有更优的性能.Compared with gray image denoising,color image denoising is more difficult,which is one of the research hotspots.Aiming at the problem of color image denoising,a color image denoising algorithm based on double weighted Schatten-p norm minimization is proposed.Firstly,the R,G and B channels are divided into blocks,and the block matrix is connected to make use of channel redundancy.Then,according to the different noise statistics in each channel,the weighted matrix is introduced to balance the data fidelity.Using the weighted Schatten-p norm as the low rank penalty term,an optimization problem with equality constraints is constructed.The alternating multiplier direction method is used to solve the problem.Each iteration update step has a closed form solution to ensure the convergence of the final result.Experimental results show that the proposed algorithm has better performance under the same conditions compared with the latest denoising algorithm.

关 键 词：彩色图像去噪 Schatten-p范数 低秩 交替乘子方向法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]