牛顿迫近迭代算法在图像恢复中的应用  

APPLICATION OF NEWTON PROXIMAL ITERATIVE ALGORITHM FOR IMAGE RESTORATION

作　　者：李旭超 刘燕[1] 李玉叶[2] 

机构地区：[1]赤峰学院计算机与信息工程学院,内蒙古赤峰024000 [2]赤峰学院数学与统计学院,内蒙古赤峰024000

出　　处：《计算机应用与软件》2017年第11期204-209,216,共7页Computer Applications and Software

基　　金：国家自然科学基金项目(11402039);2016年度内蒙古自治区科技厅自然科学基金项目(2016MS0602);2016年度内蒙古自治区高等学校科学研究项目(NJZY16254)

摘　　要：由光滑与非光滑函数构成的混合目标函数,传统的一阶优化算法,由于光滑函数一阶逼近的欠准确性和搜索步长的限制,很难获得目标函数的高精度解。针对此问题,提出二阶牛顿迫近算子分裂迭代算法。对光滑函数进行泰勒展开,获得目标函数的二阶转化模型,将转化模型分解为牛顿迭代子问题和迫近迭代子问题;给出牛顿迭代子问题的搜索方向和最优搜索步长;对算法的收敛特性进行分析。利用被系统和噪声退化的图像进行恢复实验,结果表明,该方法比现有方法峰值信噪比最高提高约2 dB,结构相似测度提高约3%。The mixture object function is composed of smooth and non-smooth function. The traditional first-order optimization algorithm is limited by the first-order approximation of the smooth function and the search step. And it is difficult to obtain a high-precision solution of the objective function. Therefore, we propose a second order Newton proximal operator splitting iterative algorithm. Firstly, Taylor expansion of the smoothing function was used to obtain the two order transformation model of the objective function. The transformed model was decomposed into Newton iterative subproblem and proximal iterative subproblem. Then, the search direction and the optimization search step length of Newton iterative sub-problem were given. Finally, the convergence property was analyzed. Taking advantage of image blurred by system and noise for restoration, we perform the recovery experiments. The results show the PSNR （peak signal to noise ratio） of the proposed method is about 2 dB higher than other methods, and the SSIM （structural similarity index measure） is improved by about 3%.

关 键 词：非光滑特性 牛顿迫近算法 迭代收敛 图像恢复 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]