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### 基于四元数非局部低秩和全变分的图像混合噪声去噪算法

1. 1.湖南大学电气与信息工程学院，湖南 长沙 410082
2.澳门大学科技学院电脑与资讯科学系，澳门 999078
• 收稿日期:2021-06-24 修回日期:2021-12-29 出版日期:2022-07-12
• 通讯作者:
• 王炼红
• 作者简介:
• 李潇瑶 女，1990年7月出生，湖南永州人.2012年在中国石油大学（北京）获得理学学士学位，现为湖南大学电气与信息工程学院硕博连读生.2017年进入澳门大学计算机与信息科学系视觉与图像处理实验室担任科研助理至今.主要研究方向为图像处理和计算机视觉.E-mail: houye0731@hnu.edu.cn
王炼红（通讯作者） 女，1971年5月出生，湖南宁乡人.副教授，硕士生导师.分别于1993年、2002年和2009年在湖南大学获得工学学士、硕士和博士学位.2011年3月至2012年3月在美国布兰迪斯大学做访问学者.主要研究方向为信号处理、数据挖掘技术、现代网络与通信技术.E-mail: 292386791@qq.com
• 基金资助:
• 国家重点研发计划 (2019YFE0105300); 国家自然科学基金 (61573299); 中国高校产学研创新基金重点项目 (2019ITA01016)

### Image Mixed Denoising Using Quaternion-Based Non-Local Low Rank and Total Variation

LI Xiao-yao1,2, WANG Lian-hong1, ZHOU Yi-cong2, ZHANG Jing1

1. 1.College of Electrical and Information Engineering，Hunan University，Changsha，Hunan 410082，China
2.Department of Computer and Information Science，University of Macau，Macau 999078，China
• Received:2021-06-24 Revised:2021-12-29 Online:2022-07-12
• Corresponding author:
• WANG Lian-hong

Abstract:

Many color image denoising methods fail to fully consider the correlations among color channels and lose many details. These always cause color distortion in the denoising results and even affect subsequent image processing tasks. In addition, the realistic noise often consists of different types of noise, such as the mixed Gaussian-impulsive noise, instead of single type. This leads to the failure of direct application in real-world image denoising for some existing denoising methods aiming at only additional Gaussian noise or only impulsive noise. To solve these problems, this paper proposes a mixed noise removal method named quaternion-based non-local low rank and total variation. The proposed method first converts the color image from spatial domain to quaternion domain, captures the non-local similarity and local gradient information and then applies the quaternion-based L1-regularized minimization model to denoise color images. Compared with many existing color denoising methods, the proposed method can keep the within-patch, cross-patch and cross-channel correlations of color images. Compared with other competing methods, the proposed method improves the peak signal-to-noise ratio and structure similarity by about 0.36~3.09 dB and 1.78%~14.55%, respectively. The visual results demonstrate the superiority of the proposed method in preserving image details and color information while removing noise and reducing artifacts. Furthermore, the proposed method is robust to noise type and noise level.