对称张量空间下高阶正则化的图像恢复模型  

High-order Regularization Model for Image Denoising in Symmetric Tensor Space

作　　者：刘孝艳[1,2] 冯象初[2] 

机构地区：[1]西安石油大学理学院,西安710065 [2]西安电子科技大学理学院数学科学系,西安710071

出　　处：《计算机科学》2013年第11A期359-362,共4页Computer Science

基　　金：国家自然科学基金(61271294;61105011;61101208);西安石油大学青年创新基金资助

摘　　要：为降低ROF模型的阶梯效应和高阶正则化方法对边缘的模糊,在对称张量空间中用二阶对称梯度构造正则项建立了新的图像去噪模型,并通过分析新模型的性质,给出了一种有效的原始-对偶算法。一方面,二阶对称梯度高于一阶导数的特性可以有效地降低阶梯效应;另一方面,二阶对称梯度模低于二阶导数模的特性能有效地保持图像的边缘等细节特征。数值仿真实验表明,新模型达到了理论分析的效果,新算法运算快捷、稳定。In order to integrative deal with staircasing effect of ROF model and over-smoothing of high-order regularization, a new model for image denoising was proposed by using second-order symmetric gradient to construct the regularization term in the symmetric tensor space. By analyzing the properties of new model, an efficient primal-dual algorithm is introduced. The new model can effectively reduce the staircase effect because the second-order symmetric gradient is higher than first derivative. Meanwhile, it can maintain the edge because the norm of second-order symmetric gradient is smaller than the norm of Hessian matrix. Both theoretical analysis and simulated results show that the new algorithm has a high converge speed and stability.

关 键 词：图像恢复 张量空间 二阶对称梯度 

分 类 号：TN911[电子电信—通信与信息系统]