基于非凸加权L_p范数稀疏误差约束的图像去噪算法

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Title:

Non-convex weighted-L_p-norm sparse-error constraint for image denoising

作者:

徐久成^1,2, 王楠^1,2, 王煜尧^1,2, 徐战威^1,2

1. 河南师范大学 计算机与信息工程学院, 河南 新乡 453007;
2. 河南省高校计算智能与数据挖掘工程技术研究中心, 河南 新乡 453007

Author(s):

XU Jiucheng^1,2, WANG Nan^1,2, WANG Yuyao^1,2, XU Zhanwei^1,2

1. College of Computer and Information Engineering, He’nan Normal University, Xinxiang 453007, China;
2. Engineering Technology Research Center for Computing Intelligence and Data Mining in Colleges and University of He’nan Province, Xinxiang 453007, C

关键词:

图像去噪; 稀疏表示; 稀疏系数; 先验知识; l₁范数; 非凸加权l_p范数; 稀疏误差约束; 峰值信噪比

Keywords:

image denoising; sparse representation; sparse coefficient; prior knowledge; l₁ norm; non-convex weighted l_p norm; sparse error constraint; peak signal-to-noise ratio

分类号:

TP391

DOI:

10.11992/tis.201804057

摘要:

图像去噪过程中由于噪声的影响，无法学习到准确的先验知识，因此难以获取较优的稀疏系数。针对该问题，本文提出一种基于非凸加权l_p范数稀疏误差约束的图像去噪算法。该算法将系数求解过程分解为两个子问题，采用广义软阈值算法求解l_p范数中的稀疏系数，再利用代理算法求解稀疏误差约束中的稀疏系数，根据二者的均值来获取更具鲁棒性的稀疏系数。与当前几种典型的算法进行对比分析，实验结果表明：本文算法不仅具有更高的峰值信噪比（PSNR），而且在运行时间上具有更高的效率，同时在视觉角度上产生了更好的视觉感受。

Abstract:

Due to noise during image denoising, it is difficult to learn accurate prior knowledge. Therefore, obtaining a desirable sparse coefficient proves to be difficult. To solve this problem, this paper proposes an image denoising method based on the non-convex weighted-l_p-norm sparse-error constraint. This algorithm decomposes the coefficient-solving process into two sub-problems. First, the algorithm solves the sparse coefficient in the l_p norm by the generalized soft threshold value algorithm and then uses the surrogate algorithm to solve the sparse coefficient in the sparse-error constraint. Finally, the algorithm obtains a robust sparse coefficient according to its average value. The experimental results show that the proposed algorithm features a high peak signal-to-noise ratio and high efficiency in terms of the running time. Simultaneously, a desirable visual perception is obtained.