一种基于曲率变分正则化的小波变换图像去噪方法

doi:10.3969/j.issn.0372-2112.2018.03.016

电子学报 ›› 2018, Vol. 46 ›› Issue (3): 621-628.DOI: 10.3969/j.issn.0372-2112.2018.03.016

一种基于曲率变分正则化的小波变换图像去噪方法

周先春^1,2,3, 吴婷¹, 石兰芳⁴, 陈铭¹

1. 南京信息工程大学电子与信息工程学院, 江苏南京 210044;
2. 儿童发展与学习科学教育部重点实验室(东南大学), 江苏南京 210009;
3. 南京信息工程大学江苏省大气环境与装备技术协同创新中心, 江苏南京 210044;
4. 南京信息工程大学数学与统计学院, 江苏南京 210044

收稿日期:2016-06-13 修回日期:2017-03-10 出版日期:2018-03-25
- 作者简介:
- 周先春,男,1974年生于安徽庐江,博士,副教授,硕士生导师,中国电子学会高级会员,研究方向为信号与信息处理.E-mail:001398@nuist.edu.cn;吴婷,女,1992年生在安徽合肥,2016年毕业于南京信息工程大学滨江学院防雷专业,现就读于南京信息工程大学,攻读电子与通信工程专业的研究生,主要研究领域为数字图像处理、模式识别;石兰芳,女,1976年生于安徽合肥,博士,副教授,硕士生导师,研究方向为非线性分析、图像处理;陈铭,男,1997年生于江苏南京,本科生,研究方向为信号处理.
- 基金资助:
- 国家自然科学基金 (No.61601229）; 江苏省"信息与通信工程"优势学科建设项目; 江苏省青蓝工程和江苏省高校自然科学研究项目 (No.13KJB170016）; 东南大学基本科研业务费资助项目 (No.CDLS-2016-03）; 江苏省研究生实践创新计划项目 (No.SJCX17-0263）

A Kind of Wavelet Transform Image Denoising Method Based on Curvature Variation Regularization

ZHOU Xian-chun^1,2,3, WU Ting¹, SHI Lan-fang⁴, CHEN Ming¹

1. College of Electronic and Information Engineering, Nanjing University of Information Science & Technology, Nanjing, Jiangsu 210044, China;
2. Key Laboratory of Child Development and Learning Science(Southeast University), Ministry of Education, Nanjing, Jiangsu 210009, China;
3. CICAEET, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China;
4. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China

Received:2016-06-13 Revised:2017-03-10 Online:2018-03-25 Published:2018-03-25
- Supported by:
- National Natural Science Foundation of China (No.61601229); Information and Communication Engineering Preponderant Discipline Development of Jiangsu Province; Blue Project in Jiangsu Province and Natural Science Research Program of Jiangsu Higher Education Institutions (No.13KJB170016); Fundamental Research Funding Project of Southeast University (No.CDLS-2016-03); Project of Jiangsu Graduate Research and Practice Innovation Program (No.SJCX17-0263)

摘要/Abstract

摘要： 噪声和图像的细节特征主要集中于图像高频部分，在图像去噪过程中，图像的某些重要特征（如边缘、细小纹理等）易受到破坏.针对这一情况，本文提出基于曲率变分正则化的小波变换图像去噪方法，首先用小波提取图像的高频成分，对图像进行增强处理，然后用增强图像的水平集曲率建立一个基于水平集曲率的曲率驱动函数，再将曲率驱动函数作为一个校正因子引入到变分模型中，建立曲率变分模型，用以控制图像的整体结构.在缺乏图像梯度信息的情况下，该模型克服了ROF模型错误扩散这一缺点，符合图像处理的形态学原则.最后，用建立的曲率变分模型处理提取的高频成分，重构处理后的高频成分和原来的低频成分，得到去噪后的图像.分析和仿真结果表明，新算法可有效抑制噪声，有极高的图像结构相似度，去噪效果明显.

关键词: 图像去噪, 变分模型, 驱动函数, 水平集曲率, 小波变换

Abstract: Image detail feature and noise mainly focus on high frequency part of image, which will make some important features of image (such as edge and fine texture) broken during image denoising. Aimed at such problems, a kind of wavelet transform image denoising method based on curvature variation regularization is set forth in this paper. Firstly, the wavelet is used to extract the high frequency part of image. Secondly, the wavelet is used to make enhancement process for images to get the enhanced image. Because the level set curvature is an important description for its morphological characters, the level set curvature of enhanced image is used to establish a curvature-driven function. Then, the curvature-driven function will be introduced to a variation model as a correction factor to establish a curvature variation model which controls the whole structure of image. This model overcomes the error diffusion caused by lack of image gradient information in ROF model and also conforms to the morphological principle of image processing. Finally, the established curvature variation model is used to process the extracted high frequency part, the wavelet reconstruction is carried out with the processed high frequency coefficients and original low frequency coefficients to get the denoised image. The analysis and simulation indicates that the method can restrict the noise in an effective way and a high similarity of image structure can be got. So a superior denoising effect can be achieved.

Key words: image denoising, variation model, driven function, level set curvature, wavelet transform

中图分类号:

TP391.41

周先春, 吴婷, 石兰芳, 等. 一种基于曲率变分正则化的小波变换图像去噪方法[J]. 电子学报, 2018, 46(3): 621-628.

ZHOU Xian-chun, WU Ting, SHI Lan-fang, et al. A Kind of Wavelet Transform Image Denoising Method Based on Curvature Variation Regularization[J]. Acta Electronica Sinica, 2018, 46(3): 621-628.

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一种基于曲率变分正则化的小波变换图像去噪方法

A Kind of Wavelet Transform Image Denoising Method Based on Curvature Variation Regularization

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