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电子学报  2015 

原始-对偶模型的牛顿迭代原理与图像恢复

DOI: 10.3969/j.issn.0372-2112.2015.10.016, PP. 1984-1993

Keywords: 原始-对偶模型,图像恢复,能量泛函,算法收敛

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Abstract:

针对非可微有界变差函数容易在图像恢复过程产生阶梯效应,提出一种二阶可微的原始-对偶模型及牛顿迭代算法.分析伪Huber函数的特性,运用Fenchel变换,将原始模型转化为原始-对偶模型,然后提出原始与对偶变量不同步长更新策略的牛顿迭代算法,并给出广义交叉验证准则确定权重.利用点扩散函数和高斯噪声对合成与真实图像进行模糊,将本文方法与快速傅里叶变换算法、快速收缩阈值算法、交替投影算法和拟牛顿算法进行实验对比,仿真表明,本文算法能保护图像的边缘,抑制阶梯效应,取得较小的相对误差、偏差,较高的峰值信噪比、相似度性测度和良好的视觉效果.

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