联合纯四元数与字典学习的彩色图像去噪方法

doi:10.12305/j.issn.1001-506X.2023.02.06

系统工程与电子技术 ›› 2023, Vol. 45 ›› Issue (2): 373-378.doi: 10.12305/j.issn.1001-506X.2023.02.06

• 电子技术 • 上一篇

联合纯四元数与字典学习的彩色图像去噪方法

曾拥华¹, 马均瑶²^,*, 黄朝燕³, 冒智慧³, 武婷婷³

1. 陆军工程大学野战工程学院, 江苏南京 210007
2. 南京邮电大学通信与信息工程学院, 江苏南京 210023
3. 南京邮电大学理学院, 江苏南京 210023

收稿日期:2021-11-25 出版日期:2023-01-13 发布日期:2023-02-04
通讯作者: 马均瑶
作者简介:曾拥华(1977—), 男, 副教授, 博士, 主要研究方向为图像处理、装备保障知识管理
马均瑶(2001—), 男, 本科, 主要研究方向为图像处理、计算机视觉
黄朝燕(1997—), 女, 硕士研究生, 主要研究方向为图像处理、机器学习
冒智慧(1998—), 女, 硕士研究生, 主要研究方向为图像处理、计算机视觉
武婷婷(1984—), 女, 副教授, 博士, 主要研究方向为图像处理, 优化方法及其应用
基金资助:
国家自然科学金(61971234);国家自然科学金(12126340);国家自然科学金(12126304);国家自然科学金(11501301);2020年江苏省研究生科研与实践创新计划(KYCX20_0788);大学生创新创业训练计划(XYB2021006)

Color image denoising method combining prue quaternion and dictionary learning

Yonghua ZENG¹, Junyao MA²^,*, Chaoyan HUANG³, Zhihui MAO³, Tingting WU³

1. College of Field Engineering, Army Engineering University, Nanjing 210007, China
2. School of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
3. School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Received:2021-11-25 Online:2023-01-13 Published:2023-02-04
Contact: Junyao MA

摘要/Abstract

摘要：

彩色图像在获取、传输和存储过程中会受到噪声的影响, 这给后续图像处理带来麻烦, 因此图像去噪任务意义重大。对此，提出一种基于四元数字典学习的模型, 该模型约束四元数的实部为零, 图像的色彩信息得以保存。传统的稀疏图像模型把彩色图像看作向量或者单色图像的线性组合, 忽略了RGB通道之间的关系。用纯四元数表示彩色图像, 将彩色图像的RGB通道表示成四元数矩阵的虚部, 拟合图像效果更好。数值实验表明, 与其他模型相比较, 所构建的模型可以更精确地表示彩色图像, 在处理彩色图像的过程中产生模型拟合误差相对较小, 峰值信噪比以及视觉效果方面均有明显提升, 能更好地进行图像去噪。

关键词: 四元数, 字典学习法, 彩色图像去噪

Abstract:

The acquisition, transmission, and storage process of color images can corrupted by noise, which brings trouble to the subsequent image processing. The task of image denoising is of great significance. A model based on quaternion dictionary learning is proposed by using the method of constraining the real part of quaternion to zero to represent color images, so that the color information can be well preserved. The traditional sparse image models only regard color image pixels as the linear connection of vector or monochrome images, which ignore the correlation of RGB channels. The color image is represented as a pure quaternion, and the RGB channels of the color image are represented as the imaginary part of the quaternion matrix, which fits the image better. Compared with other advanced models, numerical experiments show that the constructed model can represent color images more accurately, and the model fitting error is relatively small in the process of processing color images, peak signal-to-noise ratio and visual effect are significantly improved, so it can better denoise the image.

Key words: quaternion, dictionary learning method, color image denoising

中图分类号:

TP751

曾拥华, 马均瑶, 黄朝燕, 冒智慧, 武婷婷. 联合纯四元数与字典学习的彩色图像去噪方法[J]. 系统工程与电子技术, 2023, 45(2): 373-378.

Yonghua ZENG, Junyao MA, Chaoyan HUANG, Zhihui MAO, Tingting WU. Color image denoising method combining prue quaternion and dictionary learning[J]. Systems Engineering and Electronics, 2023, 45(2): 373-378.

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参考文献 30

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图像	评价指标	噪声图像	K-SVD	K-QSVD	pQS
1	SSIM PSNR	0.367 2 20.18	0.813 4 29.24	0.765 5 30.44	0.786 4 30.68
2	SSIM PSNR	0.541 2 20.17	0.858 4 26.57	0.877 3 28.89	0.888 6 29.12
3	SSIM PSNR	0.600 2 20.17	0.822 3 24.72	0.873 0 27.91	0.882 5 28.16
4	SSIM PSNR	0.621 7 20.17	0.815 0 23.75	0.849 1 27.80	0.858 6 27.87
5	SSIM PSNR	0.498 3 20.18	0.926 9 29.57	0.936 0 31.51	0.935 6 31.70
6	SSIM PSNR	0.445 2 20.17	0.837 7 27.26	0.791 4 29.54	0.797 7 29.73
7	SSIM PSNR	0.448 1 20.17	0.801 1 25.07	0.786 3 28.43	0.800 0 28.64
8	SSIM PSNR	0.526 5 20.17	0.817 5 26.58	0.791 4 28.62	0.806 1 28.79
9	SSIM PSNR	0.499 0 20.17	0.813 6 25.77	0.771 7 28.32	0.778 8 28.51
10	SSIM PSNR	0.329 3 20.17	0.820 8 29.54	0.764 9 31.72	0.762 8 31.95

图像	评价指标	噪声图像	K-SVD	K-QSVD	pQS
1	SSIM PSNR	0.244 6 17.25	0.751 7 28.04	0.690 3 28.78	0.716 5 29.06
2	SSIM PSNR	0.399 5 17.25	0.790 6 25.81	0.819 0 27.11	0.842 5 27.48
3	SSIM PSNR	0.465 6 17.25	0.790 6 24.18	0.819 0 26.24	0.833 4 26.43
4	SSIM PSNR	0.502 0 17.25	0.784 0 23.34	0.792 3 26.01	0.810 1 26.18
5	SSIM PSNR	0.367 2 17.25	0.888 1 28.23	0.909 2 29.73	0.908 0 30.05
6	SSIM PSNR	0.320 4 17.25	0.786 6 26.42	0.743 3 28.00	0.749 8 28.18
7	SSIM PSNR	0.328 1 17.25	0.749 2 24.48	0.719 2 26.67	0.732 8 26.85
8	SSIM PSNR	0.405 9 17.25	0.777 6 25.80	0.728 0 26.94	0.748 4 27.20
9	SSIM PSNR	0.382 3 17.25	0.768 0 25.14	0.711 5 26.65	0.722 4 26.93
10	SSIM PSNR	0.231 7 17.25	0.743 1 28.21	0.692 5 29.90	0.688 8 30.18

图像	评价指标	噪声图像	K-SVD	K-QSVD	pQS
1	SSIM PSNR	0.148 1 14.15	0.695 9 26.43	0.607 2 27.25	0.626 8 27.48
2	SSIM PSNR	0.279 2 14.15	0.772 9 24.67	0.769 2 25.36	0.813 8 25.75
3	SSIM PSNR	0.328 3 14.15	0.736 6 23.25	0.772 2 24.21	0.796 8 24.64
4	SSIM PSNR	0.367 9 14.16	0.732 0 22.54	0.777 1 24.03	0.798 7 24.40
5	SSIM PSNR	0.246 3 14.15	0.818 7 26.39	0.883 7 27.39	0.883 3 27.72
6	SSIM PSNR	0.209 0 14.15	0.710 7 25.12	0.689 1 26.41	0.692 8 26.65
7	SSIM PSNR	0.220 3 14.16	0.670 6 23.59	0.639 1 24.96	0.655 2 25.19
8	SSIM PSNR	0.292 3 14.15	0.721 0 24.67	0.660 8 25.30	0.680 9 25.63
9	SSIM PSNR	0.265 6 14.14	0.706 2 24.11	0.644 4 25.01	0.654 4 25.32
10	SSIM PSNR	0.154 3 14.16	0.636 2 26.50	0.775 9 28.32	0.769 7 28.49

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联合纯四元数与字典学习的彩色图像去噪方法

Color image denoising method combining prue quaternion and dictionary learning

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