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

doi:10.12263/DZXB.20210790

电子学报

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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

李潇瑶¹^,², 王炼红¹, 周怡聪², 章兢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.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

摘要/Abstract

摘要：

许多彩色图像去噪算法没有充分利用图像块间和颜色分量间的相关性，在去噪时丢失大量细节，容易导致颜色失真，从而影响后续处理.此外，真实的图像噪声通常是高斯-脉冲混合噪声而不是单一类型的，导致许多成熟的仅针对加性高斯噪声或脉冲噪声的去噪算法无法直接使用于真实场景.为解决这些问题，本文提出了基于四元数非局部低秩和全变分的图像混合噪声去除算法.该算法首先将彩色图像从空间域转换至四元数域，然后计算图像的非局部结构相似性和局部梯度，利用四元数域下的L₁范数最小化模型，最终实现图像去噪.与现有的彩色图像去噪算法相比，该算法能更有效地保留图像块间、块内以及颜色分量间的相关性.去噪实验结果表明，本文算法在峰值信噪比和结构相似性上分别提高约0.21~3.04 dB和1.51%~14.51%并能在有效去噪和抑制伪影的同时，更好地保持了图像细节和颜色信息，对噪声类型和强度变化更具鲁棒性.

关键词: 图像去噪, 混合噪声, 四元数, 非局部相似性, 低秩, 全变分

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.

Key words: image denoising, mixed noise, quaternion, non-local similarity, low rank, total variation

中图分类号:

TN911.73

李潇瑶, 王炼红, 周怡聪, 章兢. 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[J]. 电子学报, DOI: 10.12263/DZXB.20210790.

LI Xiao-yao, WANG Lian-hong, ZHOU Yi-cong, ZHANG Jing. Image Mixed Denoising Using Quaternion-Based Non-Local Low Rank and Total Variation[J]. Acta Electronica Sinica, DOI: 10.12263/DZXB.20210790.

图/表 9

图1 QNLRTV去噪算法流程图

图2 噪声强度[σ,d]为10,10%时的去噪图像

图3 噪声强度为[σ,d]为10,30%时的去噪图像

图4 噪声强度为[σ,d]为30,10%时的去噪图像

图5 去除混合噪声后的平均ΔPSNR和平均ΔSSIM

表1 去除加性噪声后的平均ΔPSNR（dB）和平均ΔSSIM

算法	噪声强度σ
算法	10	30	50
KSVD	4.92	8.08	9.12
KSVD	20.83%	41.38%	42.79%
WNNM	5.44	8.88	10.26
WNNM	21.68%	45.14%	49.01%
LSM-NLR	4.73	8.70	10.16
LSM-NLR	20.57%	43.16%	45.94%
KQSVD	4.63	8.43	9.23
KQSVD	21.16%	42.94%	43.09%
QWNNM	7.34	10.31	11.31
QWNNM	24.30%	50.30%	54.26%
QNLRTV-GN	7.47	10.52	11.59
QNLRTV-GN	25.59%	51.78%	56.03%

图6 不同参数值对PSNR的影响

图7 不同参数值对SSIM的影响

图8 QNLRTV的PSNR随迭代次数增加的变化情况

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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

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

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