Matrix-Form Neural Networks for Complex-Variable Basis Pursuit Problem With Application to Sparse Signal Reconstruction

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

11 Scopus Citations
View graph of relations

Author(s)

  • Songchuan Zhang
  • Yonghui Xia
  • Youshen Xia
  • Jun Wang

Detail(s)

Original languageEnglish
Pages (from-to)7049-7059
Journal / PublicationIEEE Transactions on Cybernetics
Volume52
Issue number7
Online published20 Jan 2021
Publication statusPublished - Jul 2022

Abstract

In this article, a continuous-time complex-valued projection neural network (CCPNN) in a matrix state space is first proposed for a general complex-variable basis pursuit problem. The proposed CCPNN is proved to be stable in the sense of Lyapunov and to be globally convergent to the optimal solution under the condition that the sensing matrix is not row full rank. Furthermore, an improved discrete-time complex projection neural network (IDCPNN) is proposed by discretizing the CCPNN model. The proposed IDCPNN consists of a two-step stop strategy to reduce the calculational cost. The proposed IDCPNN is theoretically guaranteed to be global convergent to the optimal solution. Finally, the proposed IDCPNN is applied to the reconstruction of sparse signals based on compressed sensing. Computed results show that the proposed IDCPNN is superior to related complex-valued neural networks and conventional basis pursuit algorithms in terms of solution quality and computation time.

Research Area(s)

  • Basis pursuit problem, complex state variable, matrix-form neural network, stability and global convergence

Citation Format(s)

Matrix-Form Neural Networks for Complex-Variable Basis Pursuit Problem With Application to Sparse Signal Reconstruction. / Zhang, Songchuan; Xia, Yonghui; Xia, Youshen et al.
In: IEEE Transactions on Cybernetics, Vol. 52, No. 7, 07.2022, p. 7049-7059.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review