脉冲噪声去除的L_(1)正则化方法  

L_(1) regularization method for impulse noise removal

作　　者：葛阳祖 张贵仓 黄黎明 韩根亮 宋玉哲 GE Yangzu;ZHANG Guicang;HUANG Liming;HAN Genliang;SONG Yuzhe(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China;Gansu Provincial Key Laboratory for Sensor and Sensing Technology,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070 [2]甘肃省传感器与传感技术重点实验室,甘肃兰州730070

出　　处：《现代电子技术》2022年第17期47-53,共7页Modern Electronics Technique

基　　金：国家自然科学基金项目(61861040);甘肃省科学院应用研究与开发项目(2018JK-02);甘肃省重点研发计划(20YF8GA125);甘肃省传感器与传感技术重点实验室开放基金项目(KF-6);兰州市科技计划项目(2018-4-35);甘肃省优秀研究生“创新之星”项目(2021CXZX266);西北师范大学2020年度研究生科研资助项目(2020KYZZ001127)。

摘　　要：为了实现脉冲噪声图像的复原,提出了一种基于L_(1)范数正则化模型的脉冲噪声图像复原方法。以全变差正则化模型为基础,选取L_(1)范数作为数据拟合项,加入梯度算子和小波框架作为正则化项,采用分裂Bregman迭代算法和交替方向乘子法求解模型并得到清晰图像。经证明得到由模型解得的序列是有界收敛的,且至少存在一个极值点为复原模型的稳定点。结合峰值信噪比、相对误差和结构相似度进行实验结果对比分析,结果表明采用交替方向乘子法可以有效降低复原模型的求解难度,同时该模型可以有效地去除图像脉冲噪声、抑制图像阶梯效应、保护图像边缘细节、提高峰值信噪比、减少相对误差,在结构相似度方面表现更好,在脉冲噪声图像复原中更具有普遍性,容易得到更加清晰的图像。A pulse noise image recovery method based on L_(1) norm regularization model is proposed to restore impulse noise image.On the basis of the full variation regularization model,the L_(1) norm is selected as the data fitting item,the gradient operator and wavelet frame are added into and taken as the regularization item,and the split Bregman iteration algorithm and alternating direction multiplier method are adopted to solve the model and obtain sharp images.It is proved that the sequence solved by the model is bounded convergence,and that at least one extremum point is the stability point of the restoration model.The experimental results are contrasted and analyzed in combination with peak signal-to-noise ratio(PSNR),relative error and structural similarity.The results show that the solution difficulty of the restoration model can be reduced effectively by the alternating direction multiplier method.Meanwhile,the model can effectively remove the image impulse noise,suppress the image ladder effect,protect the image edge details,increase the PSNR and reduce the relative error.In addition,it performs better in the structure similarity,and it is of more universal in the recovery of impulse noise image and can get more sharp images easily.

关 键 词：图像复原 正则化模型 脉冲噪声 分裂Bregman迭代算法 交替方向乘子法 收敛性 

分 类 号：TN911.73-34[电子电信—通信与信息系统] TP391[电子电信—信息与通信工程]