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Learning Non-Negativity Constrained Variation for Image Denoising and Deblurring

Part of: Equations of mathematical physics and other areas of application Partial differential equations

Published online by Cambridge University Press:  12 September 2017

Tengda Wei ,
Linshan Wang ,
Ping Lin ,
Jialing Chen ,
Yangfan Wang  and
Haiyong Zheng
Tengda Wei*
Affiliation:
College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao 266100, China
Linshan Wang*
Affiliation:
College of Mathematics, Ocean University of China, Qingdao 266100, China
Ping Lin*
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK
Jialing Chen*
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK
Yangfan Wang*
Affiliation:
College of Marine Life Science, Ocean University of China, Qingdao 266100, China
Haiyong Zheng*
Affiliation:
College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China
*
*Corresponding author. Email addresses:tdwei123@163.com (T. Wei), wangls@ouc.edu.cn (L. Wang), plin@maths.dundee.ac.uk (P. Lin), j.z.chen@dundee.ac.uk (J. Chen), yfwang@ouc.edu.cn (Y. Wang), zhenghaiyong@ouc.edu.cn (H. Zheng)
*Corresponding author. Email addresses:tdwei123@163.com (T. Wei), wangls@ouc.edu.cn (L. Wang), plin@maths.dundee.ac.uk (P. Lin), j.z.chen@dundee.ac.uk (J. Chen), yfwang@ouc.edu.cn (Y. Wang), zhenghaiyong@ouc.edu.cn (H. Zheng)
*Corresponding author. Email addresses:tdwei123@163.com (T. Wei), wangls@ouc.edu.cn (L. Wang), plin@maths.dundee.ac.uk (P. Lin), j.z.chen@dundee.ac.uk (J. Chen), yfwang@ouc.edu.cn (Y. Wang), zhenghaiyong@ouc.edu.cn (H. Zheng)
*Corresponding author. Email addresses:tdwei123@163.com (T. Wei), wangls@ouc.edu.cn (L. Wang), plin@maths.dundee.ac.uk (P. Lin), j.z.chen@dundee.ac.uk (J. Chen), yfwang@ouc.edu.cn (Y. Wang), zhenghaiyong@ouc.edu.cn (H. Zheng)
*Corresponding author. Email addresses:tdwei123@163.com (T. Wei), wangls@ouc.edu.cn (L. Wang), plin@maths.dundee.ac.uk (P. Lin), j.z.chen@dundee.ac.uk (J. Chen), yfwang@ouc.edu.cn (Y. Wang), zhenghaiyong@ouc.edu.cn (H. Zheng)
*Corresponding author. Email addresses:tdwei123@163.com (T. Wei), wangls@ouc.edu.cn (L. Wang), plin@maths.dundee.ac.uk (P. Lin), j.z.chen@dundee.ac.uk (J. Chen), yfwang@ouc.edu.cn (Y. Wang), zhenghaiyong@ouc.edu.cn (H. Zheng)
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Abstract

This paper presents a heuristic Learning-based Non-Negativity Constrained Variation (L-NNCV) aiming to search the coefficients of variational model automatically and make the variation adapt different images and problems by supervised-learning strategy. The model includes two terms: a problem-based term that is derived from the prior knowledge, and an image-driven regularization which is learned by some training samples. The model can be solved by classical ε-constraint method. Experimental results show that: the experimental effectiveness of each term in the regularization accords with the corresponding theoretical proof; the proposed method outperforms other PDE-based methods on image denoising and deblurring.

Keywords

Learning ideaTV-based modelconstraintε-constraint methodimage restoration

MSC classification

Secondary: 35A15: Variational methods 35Q93: PDEs in connection with control and optimization
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 4 , November 2017 , pp. 852 - 871
Copyright
Copyright © Global-Science Press 2017 

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