基于四元数组稀疏的彩色图像去噪

doi:10.11996/JG.j.2095-302X.2023020298

图学学报 ›› 2023, Vol. 44 ›› Issue (2): 298-303.DOI: 10.11996/JG.j.2095-302X.2023020298

• 图像处理与计算机视觉 • 上一篇下一篇

基于四元数组稀疏的彩色图像去噪

时妙文¹(), 范琳伟², 王桦³, 张彩明¹()

1.山东大学软件学院，山东济南 250101
2.山东财经大学计算机科学与技术学院，山东济南 250014
3.鲁东大学信息与电气工程学院，山东烟台 264025

收稿日期:2022-08-23 接受日期:2022-10-21 出版日期:2023-04-30 发布日期:2023-05-01
通讯作者: 张彩明(1955-)，男，教授，博士。主要研究方向为图形图像处理、计算机视觉等。E-mail：czhang@sdu.edu.cn
作者简介:时妙文(1988-)，女，博士研究生。主要研究方向为数字图像处理与机器学习。E-mail：shimiaowen@hotmail.com
基金资助:
国家自然科学基金项目(62072281);国家自然科学基金项目(62007017);国家自然科学基金项目(62002200);山东省自然科学基金项目(ZR2020QF012)

Quaternion patch-group sparse coding for color image denoising

SHI Miao-wen¹(), FAN Lin-wei², WANG Hua³, ZHANG Cai-ming¹()

1. School of Software, Shandong University, Jinan Shandong 250101, China
2. School of Computer Science and Technology, Shandong University of Finance and Economics, Jinan Shandong 250014, China
3. School of Information and Electrical Engineering, Ludong University, Yantai Shandong 264025, China

Received:2022-08-23 Accepted:2022-10-21 Online:2023-04-30 Published:2023-05-01
Contact: ZHANG Cai-ming (1955-), professor, Ph.D. His main research interests cover graphic image processing, computer vision, etc. E-mail：czhang@sdu.edu.cn
About author:SHI Miao-wen (1988-), PhD candidate. Her main research interests cover digital image processing and machine learning. E-mail：shimiaowen@hotmail.com
Supported by:
National Natural Science Foundation of China(62072281);National Natural Science Foundation of China(62007017);National Natural Science Foundation of China(62002200);Natural Science Foundation of Shandong Province(ZR2020QF012)

摘要/Abstract

摘要：

在采集和传播图像的过程中易受噪声的污染，从而降低了图像质量，对于后续的观察和处理产生较大影响。因此，图像去噪是当前图像处理领域一个重要的课题，其关键问题是如何在去除噪声的同时保留图像信息。由于图像具有自相似性，一般的图像去噪方法是利用组稀疏来重建图像。对于彩色图像提出了基于四元数组稀疏的去噪算法。首先，用四元数的形式来描述图像中的每个像素，从而构造出图像块组。在此基础上，该模型对每个图像块进行了更新，并用词字典中的线性组合对每个图像块组进行描述。为了进一步提高重构后的图像结构信息的准确性，结合了组稀疏模型和核维纳滤波器。核维纳滤波的基准影像是由组稀疏表达所获得的结果。与传统的方法比较，该模型既能将3种颜色通道的关联结合起来，又能使各图像块组间的关联性得到最大程度的发挥。实验表明，采用该方法重构的图像在不同的噪声等级下量化指标和视觉效果均有较好表现。

关键词: 图像去噪, 四元数分析, 图像块匹配, 主成分分析, 稀疏表示

Abstract:

Images are inevitably corrupted by noise during transition and acquisition, which exerts a considerable influence on the subsequent processing. Therefore, image denoising is essential for image processing. Specially, the critical challenge of image denoising is to remove the noise while preserving information as much as possible. Generally, the group-based sparse representation model is exploited to restore the clean image, due to the self-similarity of natural images. This paper offered a novel color image denoising method that utilized quaternions in the group sparsity model, where each pixel was expressed as a pure quaternion. Initially, each pixel of the observed image was expressed as a quaternion unit, and a quaternion patch group matrix was established by Pearson′s correlation coefficient. The proposed model then learnt the dictionary for each patch group, working well with the pursuit algorithm. In other words, the group-based sparsity method assumed that each patch group was a linear combination of the basic elements of the dictionary. Unfortunately, it remained arduous to reconstruct the image structure precisely. Therefore, the group sparsity model incorporated kernel Wiener filtering to enhance image structure quality. In contrast to the traditional models, the new model not only worked with the corresponding RGB channels, but also leveraged the relationship between patches. Fueled by the exploration of the inner correlation of color channels, the proposed method could preserve the image information as much as possible while removing noise. The experiments validated the efficiency of the proposed method both in numerical results and visual performance on different noise levels.

Key words: image denoising, quaternion analysis, patch grouping, principal component analysis, sparse representation

中图分类号:

TP391

时妙文, 范琳伟, 王桦, 张彩明. 基于四元数组稀疏的彩色图像去噪[J]. 图学学报, 2023, 44(2): 298-303.

SHI Miao-wen, FAN Lin-wei, WANG Hua, ZHANG Cai-ming. Quaternion patch-group sparse coding for color image denoising[J]. Journal of Graphics, 2023, 44(2): 298-303.

图/表 4

参考文献 23

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σ	方法	Airplane	Baboon	Barbara	Boats	Butterfly	House	Lena	Peppers
10	BM3D	33.72	30.12	33.36	33.25	33.13	35.59	34.37	34.34
	QKSVD	33.14	28.26	31.71	32.51	32.43	34.18	33.29	33.44
	QMNLM	30.12	28.27	31.45	29.83	28.53	34.34	31.92	31.12
	本文	33.98	30.30	33.74	33.55	34.01	35.86	34.56	34.62
30	BM3D	27.71	23.57	27.64	27.10	27.26	31.59	28.66	28.85
	QKSVD	27.82	23.60	26.74	27.07	26.90	29.91	28.24	28.22
	QMNLM	25.72	24.20	26.00	25.25	24.73	27.88	26.61	26.28
	本文	28.08	23.85	27.98	27.45	28.04	31.90	29.03	29.17
50	BM3D	25.19	21.34	25.20	24.49	24.35	29.29	26.08	26.14
	QKSVD	25.04	21.56	24.32	24.46	24.32	27.46	25.67	25.50
	QMNLM	22.42	22.07	22.84	22.04	19.67	24.34	23.26	22.92
	本文	25.64	21.75	25.49	25.00	25.51	29.78	26.54	26.59

σ	方法	Airplane	Baboon	Barbara	Boats	Butterfly	House	Lena	Peppers
10	BM3D	33.72	30.12	33.36	33.25	33.13	35.59	34.37	34.34
	QKSVD	33.14	28.26	31.71	32.51	32.43	34.18	33.29	33.44
	QMNLM	30.12	28.27	31.45	29.83	28.53	34.34	31.92	31.12
	本文	33.98	30.30	33.74	33.55	34.01	35.86	34.56	34.62
30	BM3D	27.71	23.57	27.64	27.10	27.26	31.59	28.66	28.85
	QKSVD	27.82	23.60	26.74	27.07	26.90	29.91	28.24	28.22
	QMNLM	25.72	24.20	26.00	25.25	24.73	27.88	26.61	26.28
	本文	28.08	23.85	27.98	27.45	28.04	31.90	29.03	29.17
50	BM3D	25.19	21.34	25.20	24.49	24.35	29.29	26.08	26.14
	QKSVD	25.04	21.56	24.32	24.46	24.32	27.46	25.67	25.50
	QMNLM	22.42	22.07	22.84	22.04	19.67	24.34	23.26	22.92
	本文	25.64	21.75	25.49	25.00	25.51	29.78	26.54	26.59

基于四元数组稀疏的彩色图像去噪

Quaternion patch-group sparse coding for color image denoising

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