Quaternion-Based Dictionary Learning and Saturation-Value Total Variation Regularization for Color Image Restoration | IEEE Journals & Magazine | IEEE Xplore

Quaternion-Based Dictionary Learning and Saturation-Value Total Variation Regularization for Color Image Restoration


Abstract:

Color image restoration is a critical task in imaging sciences. Most variational methods regard the color image as a Euclidean vector or the direct combination of three m...Show More

Abstract:

Color image restoration is a critical task in imaging sciences. Most variational methods regard the color image as a Euclidean vector or the direct combination of three monochrome images and completely ignore the inherent color structures within channels. To better describe the relationship of color channels, we represent the color image as the so-called pure quaternion matrix. Note that the celebrated dictionary learning method has attracted considerable attention for image recovery in the past decade. Following this idea, we propose a novel quaternion-based color image recovery method. This model combines the advantages of dictionary learning and the total variation method for color image restoration. The new strategy used in the proposed model manages to handle the color image restoration problem in the quaternion space. Moreover, the new proposed model can be easily solved by the classical alternating direction method of multipliers (ADMM) algorithm. Numerical results demonstrate clearly that the performance of our proposed dictionary learning method is better than some state-of-the-art color image dictionary learning and total variation methods in terms of some criteria and visual quality.
Published in: IEEE Transactions on Multimedia ( Volume: 24)
Page(s): 3769 - 3781
Date of Publication: 27 August 2021

ISSN Information:

Funding Agency:

Author image of Chaoyan Huang
School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China
Chaoyan Huang received the B.S. degree with the College of Mathematics and Computer Science, Anqing Normal University, Anqing, China, in 2019. She is currently working toward the M.S. degree with the School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China. Her research interests include image processing, inverse problems, and machine learning.
Chaoyan Huang received the B.S. degree with the College of Mathematics and Computer Science, Anqing Normal University, Anqing, China, in 2019. She is currently working toward the M.S. degree with the School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China. Her research interests include image processing, inverse problems, and machine learning.View more
Author image of Michael K. Ng
Department of Mathematics, The University of Hong Kong, Hong Kong
Michael K. Ng received the B.Sc. and M.Phil. degrees from the University of Hong Kong, Hong Kong, in 1990 and 1992, respectively, and the Ph.D. degree from the Chinese University of Hong Kong, Hong Kong, in 1995. He is currently a Chair Professor with the Department of Mathematics, University of Hong Kong. His research interests include bioinformatics, image processing, scientific computing, and data mining.
Michael K. Ng received the B.Sc. and M.Phil. degrees from the University of Hong Kong, Hong Kong, in 1990 and 1992, respectively, and the Ph.D. degree from the Chinese University of Hong Kong, Hong Kong, in 1995. He is currently a Chair Professor with the Department of Mathematics, University of Hong Kong. His research interests include bioinformatics, image processing, scientific computing, and data mining.View more
Author image of Tingting Wu
School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China
Tingting Wu received the B.S. and Ph.D. degrees in mathematics from Hunan University, Changsha, China, in 2006 and 2011, respectively. From 2015 to 2018, she was a Postdoctoral Researcher with the School of Mathematical Sciences, Nanjing Normal University, Nanjing, China. From 2016 to 2017, she was a Research Fellow with Nanyang Technological University, Singapore. She is currently an Associate Professor with the School o...Show More
Tingting Wu received the B.S. and Ph.D. degrees in mathematics from Hunan University, Changsha, China, in 2006 and 2011, respectively. From 2015 to 2018, she was a Postdoctoral Researcher with the School of Mathematical Sciences, Nanjing Normal University, Nanjing, China. From 2016 to 2017, she was a Research Fellow with Nanyang Technological University, Singapore. She is currently an Associate Professor with the School o...View more
Author image of Tieyong Zeng
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
Tieyong Zeng received the B.S. degree from Peking University, Beijing, China, in 2000, the M.S. degree from École Polytechnique, Palaiseau, France, in 2004, and the Ph.D. degree from the University of Paris XIII, Paris, France, in 2007. He was a Postdoctoral Researcher with ENS de Cachan, Cachan, France, since 2007 to 2008, and an Assistant/Associate Professor with Hong Kong Baptist University, Hong Kong, since 2008 to 20...Show More
Tieyong Zeng received the B.S. degree from Peking University, Beijing, China, in 2000, the M.S. degree from École Polytechnique, Palaiseau, France, in 2004, and the Ph.D. degree from the University of Paris XIII, Paris, France, in 2007. He was a Postdoctoral Researcher with ENS de Cachan, Cachan, France, since 2007 to 2008, and an Assistant/Associate Professor with Hong Kong Baptist University, Hong Kong, since 2008 to 20...View more

Author image of Chaoyan Huang
School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China
Chaoyan Huang received the B.S. degree with the College of Mathematics and Computer Science, Anqing Normal University, Anqing, China, in 2019. She is currently working toward the M.S. degree with the School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China. Her research interests include image processing, inverse problems, and machine learning.
Chaoyan Huang received the B.S. degree with the College of Mathematics and Computer Science, Anqing Normal University, Anqing, China, in 2019. She is currently working toward the M.S. degree with the School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China. Her research interests include image processing, inverse problems, and machine learning.View more
Author image of Michael K. Ng
Department of Mathematics, The University of Hong Kong, Hong Kong
Michael K. Ng received the B.Sc. and M.Phil. degrees from the University of Hong Kong, Hong Kong, in 1990 and 1992, respectively, and the Ph.D. degree from the Chinese University of Hong Kong, Hong Kong, in 1995. He is currently a Chair Professor with the Department of Mathematics, University of Hong Kong. His research interests include bioinformatics, image processing, scientific computing, and data mining.
Michael K. Ng received the B.Sc. and M.Phil. degrees from the University of Hong Kong, Hong Kong, in 1990 and 1992, respectively, and the Ph.D. degree from the Chinese University of Hong Kong, Hong Kong, in 1995. He is currently a Chair Professor with the Department of Mathematics, University of Hong Kong. His research interests include bioinformatics, image processing, scientific computing, and data mining.View more
Author image of Tingting Wu
School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China
Tingting Wu received the B.S. and Ph.D. degrees in mathematics from Hunan University, Changsha, China, in 2006 and 2011, respectively. From 2015 to 2018, she was a Postdoctoral Researcher with the School of Mathematical Sciences, Nanjing Normal University, Nanjing, China. From 2016 to 2017, she was a Research Fellow with Nanyang Technological University, Singapore. She is currently an Associate Professor with the School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China. Her research interests include variational methods for image processing and computer vision, optimization methods and their applications in sparse recovery, and regularized inverse problems.
Tingting Wu received the B.S. and Ph.D. degrees in mathematics from Hunan University, Changsha, China, in 2006 and 2011, respectively. From 2015 to 2018, she was a Postdoctoral Researcher with the School of Mathematical Sciences, Nanjing Normal University, Nanjing, China. From 2016 to 2017, she was a Research Fellow with Nanyang Technological University, Singapore. She is currently an Associate Professor with the School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China. Her research interests include variational methods for image processing and computer vision, optimization methods and their applications in sparse recovery, and regularized inverse problems.View more
Author image of Tieyong Zeng
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
Tieyong Zeng received the B.S. degree from Peking University, Beijing, China, in 2000, the M.S. degree from École Polytechnique, Palaiseau, France, in 2004, and the Ph.D. degree from the University of Paris XIII, Paris, France, in 2007. He was a Postdoctoral Researcher with ENS de Cachan, Cachan, France, since 2007 to 2008, and an Assistant/Associate Professor with Hong Kong Baptist University, Hong Kong, since 2008 to 2018. He is currently a Professor with the Department of Mathematics, The Chinese University of Hong Kong, Hong Kong. His research interests include image processing, machine learning, and scientific computing.
Tieyong Zeng received the B.S. degree from Peking University, Beijing, China, in 2000, the M.S. degree from École Polytechnique, Palaiseau, France, in 2004, and the Ph.D. degree from the University of Paris XIII, Paris, France, in 2007. He was a Postdoctoral Researcher with ENS de Cachan, Cachan, France, since 2007 to 2008, and an Assistant/Associate Professor with Hong Kong Baptist University, Hong Kong, since 2008 to 2018. He is currently a Professor with the Department of Mathematics, The Chinese University of Hong Kong, Hong Kong. His research interests include image processing, machine learning, and scientific computing.View more

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