DOUBLE INERTIAL PARAMETERS FORWARD-BACKWARD SPLITTING METHOD: APPLICATIONS TO COMPRESSED SENSING, IMAGE PROCESSING, AND SCAD PENALTY PROBLEMS

Lateef Olakunle Jolaoso, Yekini Shehu*, Jen Chih Yao, Renqi Xu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this paper, a forward-backward splitting algorithm with two inertial parameters (one non-negative and the other non-positive) extrapolation step is proposed for finding a zero point of the sum of maximal monotone and co-coercive operators in real Hilbert spaces. One of the interesting features of our proposed algorithm is that no online rule on the inertial parameters with the iterates is needed. The weak convergence result of the proposed algorithm is established under some standard assumptions. Numerical results arising from LASSO problems in compressed sensing, image processing, and SCAD penalty problems are provided to illustrate the behavior of our proposed algorithm.

Original languageEnglish
Pages (from-to)627-646
Number of pages20
JournalJournal of Nonlinear and Variational Analysis
Volume7
Issue number4
DOIs
Publication statusPublished - 1 Aug 2023
Externally publishedYes

Keywords

  • Compressed sensing
  • Forward-backward splitting
  • Image processing
  • Two-step inertial
  • Weak convergence

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