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Two Matrix-Type Projection Neural Networks for Matrix-Valued Optimization with Application to Image Restoration

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Abstract

In recent years, matrix-valued optimization algorithms have been studied to enhance the computational performance of vector-valued optimization algorithms. This paper presents two matrix-type projection neural networks, continuous-time and discrete-time ones, for solving matrix-valued optimization problems. The proposed continuous-time neural network may be viewed as a significant extension to the vector-type double projection neural network. More importantly, the proposed discrete-time projection neural network is suitable for parallel implementation in terms of matrix state spaces. Under pseudo-monotonicity and Lipschitz continuous conditions, the proposed two matrix-type projection neural networks are guaranteed to be globally convergent to the optimal solution. Finally, the proposed matrix-type projection neural network is effectively applied to image restoration. Computed examples show that the two proposed matrix-type projection neural networks are much superior to the vector-type projection neural networks in terms of computation speed.

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Authors and Affiliations

  1. Department of Basic Teaching and Research, Yango University, Fuzhou, China

    Lingmei Huang

  2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China

    Youshen Xia & Liqing Huang

  3. College of Mathematics and Computer Science, Wuyi University, Nanping, China

    Songchuan Zhang

Authors
  1. Lingmei Huang
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  2. Youshen Xia
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  3. Liqing Huang
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  4. Songchuan Zhang
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Correspondence to Youshen Xia.

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This work is supported by the National Natural Science Foundation of China under Grant No. 61473330.

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Huang, L., Xia, Y., Huang, L. et al. Two Matrix-Type Projection Neural Networks for Matrix-Valued Optimization with Application to Image Restoration. Neural Process Lett 53, 1685–1707 (2021). https://doi.org/10.1007/s11063-019-10086-w

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