Inverse-free distributed neurodynamic optimization algorithms for sparse reconstruction

Xin HAN, Xing HE*, Mingliang ZHOU, Tingwen HUANG

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

1 Citation (Scopus)


This article proposes three novel inverse-free distributed neurodynamic optimization algorithms to reconstruct sparse signal and image by addressing the L1-minimization problems. Based on multi-agent consensus theory, we successfully transform the original L1-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 languageEnglish
Article number109360
Number of pages13
JournalSignal Processing
Publication statusPublished - May 2024
Externally publishedYes

Bibliographical note

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).


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


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