A Fast Algorithm for Matrix-Variable Triconvex Optimization With Application to Blind Image Deblurring

Songchuan Zhang; Liqing Huang; Youshen Xia; Jun Wang

doi:10.1109/JAS.2026.125711

Volume 13 Issue 5

May 2026

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 19.2, Top 1 (SCI Q1)

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(5): 1184-1206

S. Zhang, L. Huang, Y. Xia, and J. Wang, “A fast algorithm for matrix-variable triconvex optimization with application to blind image deblurring,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 5, pp. 1184–1206, May 2026. doi: 10.1109/JAS.2026.125711

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S. Zhang, L. Huang, Y. Xia, and J. Wang, “A fast algorithm for matrix-variable triconvex optimization with application to blind image deblurring,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 5, pp. 1184–1206, May 2026. doi: 10.1109/JAS.2026.125711

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A Fast Algorithm for Matrix-Variable Triconvex Optimization With Application to Blind Image Deblurring

doi: 10.1109/JAS.2026.125711

Funds: This work was supported by the National Natural Science Foundation of China (62276140), the Natural Science Foundation of Fujian Province (2021J011148, 2022J01190), and Hong Kong Research Grants Council (AoE/E-407/24-N, C1013-24GF)

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Author Bio:
Songchuan Zhang received the B.Sc. degree in mathematics from Fujian Normal University in 1999, the M.Sc. degree in applied mathematics from Fuzhou University in 2005, and the Ph.D. degree in applied mathematics with the Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University in 2016.Dr. Zhang received the Outstanding Doctoral Dissertations Award of Fujian Province in 2016. He is currently a Professor with Fujian Key Laboratory of Big Data Application and Intellectualization for Tea Industry, College of Mathematics and Computer, Wuyi University. His current research interests include neural networks, computational intelligence, and optimization theory and their applications

Liqing Huang received the B.D., M.D., and Ph.D. degrees in computer science from Fuzhou University, in 2014, 2017, and 2020, respectively.She is a Lecturer with the College of Computer and Cyber Security, Fujian Normal University. And she currently engaged in postdoctoral research at Nanjing University of Information Technology. Her research interests include image, video processing, and neural networks

Youshen Xia received the B.Sc. and M.Sc. degrees in computational mathematics from Nanjing University, respectively in 1982 and 1989, and the Ph.D. degree in automation and computer-aided engineering from the Chinese University of Hong Kong, China, in 2000.Dr. Xia held research/visiting positions at the Chinese University of Hong Kong, City University of Hong Kong, Calgary University, Canada, the University of Waterloo, Canada, and the University of Western Australia, Australia. From 2007 to 2020. He was a Distinguished Professor with Fuzhou University. At present, he is a Distinguished Professor with the College of Artificial Intelligence, Anhui University. Dr. Xia was a recipient of the three natural science awards from the Ministry of Education of China in 2010, the Fujian Province of China in 2017, and the China Automation Society in 2019. His current research interests include design and analysis of neural dynamical optimization methods, blind image restoration, enhancement, and super resolution

Jun Wang (Life Fellow, IEEE) received the B.S. degree in electrical engineering, the M.S. degree in systems engineering from Dalian University of Technology in 1982 and 1985, respectively, and the Ph.D. degree in systems engineering from Case Western Reserve University, Cleveland, OH, USA, in 1991. He held various academic positions at Dalian University of Technology; Case Western Reserve University, Cleveland; University of North Dakota, Grand Forks, ND, USA; and The Chinese University of Hong Kong, Hong Kong, China. He also held various short-term or part-time visiting positions at USA; Air Force Armstrong Laboratory, Dayton, OH, USA; RIKEN Brain Science Institute, Tokyo, Japan; Huazhong University of Science and Technology; Shanghai Jiao Tong University; Dalian University of Technology; and Swinburne University of Technology, Melbourne, VIC, Australia. He is currently a Chair Professor with City University of Hong Kong, Hong Kong, China. Dr. Wang was a recipient of several awards such as the Research Excellence Award from the Chinese University of Hong Kong from 2008 to 2009, the Outstanding Achievement Award from Asia-Pacific Neural Network Assembly in 2011, IEEE Transactions on Neural Networks Outstanding Paper Award in 2011, the Neural Networks Pioneer Award from the IEEE Computational Intelligence Society in 2014, and the Norbert Wiener Award from the IEEE Systems, Man, and Cybernetics Society in 2019. He has been the Editor-in-Chief of the IEEE Transactions on Artificial Intelligence since 2025 and was the Editor-in-Chief of the IEEE Transactions on Cybernetics from 2014 to 2019. He served as the General Chair of the 13th/25th International Conference on Neural Information Processing in 2006/2018 and the IEEE World Congress on Computational Intelligence in 2008. He was a Distinguished Lecturer of the IEEE Systems, Man, and Cybernetics Society from 2017 to 2022 and the IEEE Computational Intelligence Society from 2010 to 2012 and 2014 to 2016
Corresponding author: Youshen Xia, e-mail: ysxia@fzu.edu.cn
¹ Photo CD PCD0992: https://r0k.us/graphics/kodak/
² Berkeley dataset (BSDS500): https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/resources.html
Received Date: 2024-11-14
Revised Date: 2025-02-04
Accepted Date: 2025-10-25

Abstract

Abstract

Matrix-variable triconvex optimization is a significant generalization of vector-variable triconvex or biconvex optimization and has been found to have popular applications. To reduce computation time and storage requirements, this paper presents a matrix-form iterative method for quickly solving matrix-variable constrained triconvex optimization problems. The proposed method is based on a matrix-form alternating projection iteration scheme in the form of matrix state spaces, where an efficient line search strategy is adopted by exploiting the optimality conditions of the problem for a larger step length. Compared with the existing vector-form alternating projection gradient method, the proposed method reduces storage requirements and computational cost, and thus is more computationally efficient. Each sequence generated by the proposed method is guaranteed to be globally convergent to a partial optimum under mild conditions. Finally, the proposed method is effectively applied to blind image deblurring problems. Computed results show that the proposed algorithm is superior to related iterative algorithms in terms of computation time and solution quality.
- Blind image deblurring,
- global convergence,
- matrix-form iterative method,
- matrix variable,
- multiconvex optimization

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¹ Photo CD PCD0992: https://r0k.us/graphics/kodak/
² Berkeley dataset (BSDS500): https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/resources.html

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