## Abstract

This article proposes three novel inverse-free distributed neurodynamic optimization algorithms to reconstruct sparse signal and image by addressing the L_{1}-minimization problems. Based on multi-agent consensus theory, we successfully transform the original L_{1}-minimization problem into a distributed optimization model. To tackle such model, a three-layer inverse-free distributed algorithm is proposed by using projection operator and derivative feedback, which enjoys global convergence. To simplify the structure of this three-layer distributed algorithm, a time-varying parameter-based two-layer inverse-free distributed algorithm is designed, which has global convergence. Moreover, to accelerate convergence and further simplify the structure of this two-layer distributed algorithm, we develop a Tikhonov-like regularization-based single-layer inverse-free distributed algorithm, which achieves consensus within finite time for any given initial point and possesses an O(1/ξ(t)) convergence rate of the linear-equality constraint function. Finally, experimental results on signal and image reconstruction are presented to illustrate the efficiency of our inverse-free distributed algorithms.

Original language | English |
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Article number | 109360 |

Number of pages | 13 |

Journal | Signal Processing |

Volume | 218 |

DOIs | |

Publication status | Published - May 2024 |

Externally published | Yes |

### Bibliographical note

Acknowledgments:This work was supported by the National Natural Science Foundation of China (62176218), the Fundamental Research Funds for the Central Universities (XDJK2020TY003), and in part by the General Research Foundation for Dazhou Mathematics and Finance Center of China (SCMF202206).

## Keywords

- Finite-time consensus and global convergence rate
- Global convergence
- Inverse-free distributed neurodynamic optimization method
- Signal and image restoration