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A Neurodynamic Algorithm for Sparse Signal Reconstruction with Finite-Time Convergence

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Abstract

In this paper, a neurodynamic algorithm with finite-time convergence to solve \({L_{\mathrm{{1}}}}\)-minimization problem is proposed for sparse signal reconstruction which is based on projection neural network (PNN). Compared with the existing PNN, the proposed algorithm is combined with the sliding mode technique in control theory. Under certain conditions, the stability of the proposed algorithm in the sense of Lyapunov is analyzed and discussed, and then the finite-time convergence of the proposed algorithm is proved and the setting time bound is given. Finally, simulation results on a numerical example and a contrast experiment show the effectiveness and superiority of our proposed neurodynamic algorithm.

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Acknowledgements

This work is supported by Natural Science Foundation of China (Grant Nos: 61773320) and Fundamental Research Funds for the Central Universities (Grant No. XDJK2020TY003) and also supported by the Natural Science Foundation Project of Chongqing CSTC (Grant No. cstc2018jcyjAX0583).

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Authors and Affiliations

  1. Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Hongsong Wen & Xing He

  2. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Hui Wang

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  1. Hongsong Wen
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  2. Hui Wang
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  3. Xing He
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Correspondence to Hui Wang or Xing He.

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Wen, H., Wang, H. & He, X. A Neurodynamic Algorithm for Sparse Signal Reconstruction with Finite-Time Convergence. Circuits Syst Signal Process 39, 6058–6072 (2020). https://doi.org/10.1007/s00034-020-01445-3

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