Analysis and Application of a Discrete-Time Neurodynamic Approach for Fast Constrained <i>l</i><sub>1</sub>-Norm Minimization

Youshen Xia; Jun Wang; Changyin Sun

doi:10.1109/JAS.2026.125729

IEEE/CAA Journal of Automatica Sinica

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Y. Xia, J. Wang, and C. Sun, “Analysis and application of a discrete-time neurodynamic approach for fast constrained l1-norm minimization,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 3, pp. 1–14, Mar. 2026. doi: 10.1109/JAS.2026.125729

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Y. Xia, J. Wang, and C. Sun, “Analysis and application of a discrete-time neurodynamic approach for fast constrained l₁-norm minimization,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 3, pp. 1–14, Mar. 2026. doi: 10.1109/JAS.2026.125729

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Analysis and Application of a Discrete-Time Neurodynamic Approach for Fast Constrained l₁-Norm Minimization

doi: 10.1109/JAS.2026.125729

Funds: This work was supported by the National Natural Science Foundation of China (62276140), and in part by the National Natural ScienceFoundation of China (62236002, 62495083), and in part by Hong Kong Research Grants Council ( AoE/E-407/24-N, C1013-24GF)

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Author Bio:
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, China, 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 and image restoration

Jun Wang (Life Fellow) 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 U.S. 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 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

Changyin Sun (Senior Member) received the B.S. degree in applied mathematics from Sichuan University in 1996, and the M.S. and Ph.D. degrees in electrical engineering from Southeast University in 2001 and 2004, respectively. He is currently a Professor with the School of Artificial Intelligence, Anhui University. His research interests include intelligent control, flight control, and optimal theory. Professor Sun is an Associate Editor of IEEE Transactions on Neural Networks and Learning Systems, Neural Processing Letters, and IEEE/CAA Journal of Automatica Sinica
Corresponding author: Youshen Xia, e-mail: ysxia@ahu.edu.cn
Received Date: 2025-06-13
Accepted Date: 2025-11-04

Available Online: 2026-03-09

Abstract

Abstract

Discrete-time neurodynamic approaches (also called recurrent neural networks (RNNs)) are easily implemented on software and simulated on digital circuits. First, this paper proposes two modified discrete-time RNNs for quickly dealing with constrained $l_1$-norm minimization problems. Next, the two modified discrete-time RNNs are proven to be globally convergent to an optimal solution under a large step size. Finally, we apply the obtained results for image recovery. Two convergent discrete-time RNN based algorithms for non-blind image restoration are presented. Due to having a low complexity, the two discrete-time RNNs are more computationally efficient than the existing discrete-time RNN for image restoration. Computed results with application examples show that the two discrete-time RNN-based algorithms are indeed superior to the existing discrete-time RNN-based algorithms with regards to computation time.
- Constrained the $l_1$-norm minimization,
- convergence analysis,
- discrete-time neurodynamic approach,
- fixed step length,
- image recovery

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References(42)

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Analysis and Application of a Discrete-Time Neurodynamic Approach for Fast Constrained l1-Norm Minimization

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Analysis and Application of a Discrete-Time Neurodynamic Approach for Fast Constrained l₁-Norm Minimization