基于Moreau包络平滑l1/全变差范数模型的图像脉冲噪声去除方法

脉冲噪声是导致图像退化的主要原因之一，低密度脉冲噪声去除比较容易，但高密度比较困难。为了有效去除高密度的脉冲噪声，提高边缘和细节纹理的保持能力，提出了一种基于莫罗(Moreau)包络平滑l1/全变差范数(l1/TV)模型的脉冲噪声去除方法。此方法具有修复前后图像对比度和形态不变，不易产生局部模糊等优点。由于l1/TV模型中的两个目标函数均为不可微凸函数，无法直接求解，提出了利用解耦形式的Moreau包络对全变差范数进行平滑化处理，平滑后的函数是原函数的可微紧下界，具有迭代形式的解析解，证明了它也是原函数的解。仿真表明该算法具有很强的去噪能力，并能较好地保持边缘和细节信息。此外，还提出了该算法的加速策略，可以大大提高收敛速度。

Abstract

Impulse noise is one of the main causes of image degradation, low density impulse noise can be easily removed while high density impulse noise removal is more difficult. In order to effectively remove high density impulse noise and to keep edges and texture better, an algorithm based on Moreau envelope smoothing l1/total variation (l1/TV) norm model is proposed. This algorithm has advantages such as contrast and morphological invariance and absence of local blur. Since the convex objective function in l1/TV model is non-differentiable and thus difficult to solve, smoothing the total variation part by utilizing decoupled Moreau envelope is proposed. As the smoothed function which generates an iterative form of analytical solution is the differentiable tight lower bound of the original function, it is provable that they have the same solution. The simulation results show that the algorithm effectively removes noise with edges and texture kept. In addition, the combined acceleration steps are proposed to greatly improve the speed of convergence.

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王斌, 胡辽林, 曹京京, 薛瑞洋, 王亚萍. 基于Moreau包络平滑l1/全变差范数模型的图像脉冲噪声去除方法[J]. 光学学报, 2014, 34(12): 1211002. Wang Bin, Hu Liaolin, Cao Jingjing, Xue Ruiyang, Wang Yaping. Impulse Noise Removal Method Based on Moreau Envelope Smoothing l1/TV Norm Model[J]. Acta Optica Sinica, 2014, 34(12): 1211002.

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