基于增广拉格朗日乘子的快速高阶全变分图像去噪方法

高阶全变分图像去噪方法利用图像方向导数的可分L1范数,构建优化方程进行图像去噪,可以在去除图像噪声的同时有效保留图像中的细节信息。然而传统高阶全变分方法计算复杂度较高、耗时较长。针对此问题,提出了一种基于增广拉格朗日乘子的快速高阶全变分图像去噪方法。首先,利用Huber方程重建高阶全变分优化方程;其次,通过添加辅助变量及引入拉格朗日乘子,将优化方程转换为两个较易求解的子问题进行交替最小化迭代求解。实验证明,在相同条件下,与传统方法相比,基于增广拉格朗日乘子的高阶全变分图像去噪方法可以大幅提高运算速度,并且能在去除图像噪声的同时更好地保留图像边缘、纹理、细节等信息,获得视觉效果更好的去噪图像。

Augmented Lagrangian multiplier based fast higher degree total variation image denoising algorithm#br#

Higher degree total variation (HDTV) denoising algorithm is the fully separable L1 norm of the image directional derivatives. The usage of this denoising algorithm is seen to effectively denoise images while preserving details and features in the image. However, the traditional HDTV method has the disadvantage of low computation speed due to the comparatively high computational complexity. An augmented Lagrangian multiplier based fast HDTV image denoising algorithm is introduced. Firstly, the Huber function is used to reformulate the HDTV optimization function. Secondly, by introducing the auxiliary variable and the Lagrangian multiplier, the original problem is converted into two sub problems which can be solved using the alternating minimization method efficiently. The results demonstrate that compared with the traditional algorithm, the proposed algorithm is able to obtain ten times speedup. Besides, the proposed algorithm is able to better preserve the image details and edges information.