基于增广拉格朗日乘子的快速高阶全变分图像去噪方法

发布时间：2018-06-19 08:36

本文选题：高阶全变分 + 图像去噪　；参考：《系统工程与电子技术》2017年12期

【摘要】：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。
[Abstract]:High-order total variational image denoising method uses the divisible L1 norm of the directional derivative of the image to construct an optimization equation for image denoising, which can effectively preserve the details of the image while removing the image noise. However, the computational complexity of the traditional high order total variational method is higher and the time consuming is longer. To solve this problem, a fast high order total variational image denoising method based on augmented Lagrangian multiplier is proposed. Firstly, the Huber equation is used to reconstruct the higher order total variational optimization equation. Secondly, by adding auxiliary variables and introducing Lagrange multiplier, the optimization equation is transformed into two subproblems which are easy to solve and are solved by alternating minimization iteration. Experiments show that under the same conditions, compared with the traditional method, the denoising method based on augmented Lagrangian multiplier can greatly improve the computation speed and preserve the edge of the image while removing the image noise. Texture, details and other information to obtain a better visual effect of denoising image.
【作者单位】：哈尔滨工业大学电子与信息工程学院;中船重工第七0三研究所;
【基金】：国家自然科学基金(61501146) 黑龙江省自然科学基金面上项目(F2016018)资助课题
【分类号】：TP391.41

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