Signal reconstruction by conjugate gradient algorithm based on smoothing l1 -norm

Caiying Wu, Jiaming Zhan, Yue Lu, Jein Shan Chen

Research output: Contribution to journalArticle

Abstract

The l1-norm regularized minimization problem is a non-differentiable problem and has a wide range of applications in the field of compressive sensing. Many approaches have been proposed in the literature. Among them, smoothing l1-norm is one of the effective approaches. This paper follows this path, in which we adopt six smoothing functions to approximate the l1-norm. Then, we recast the signal recovery problem as a smoothing penalized least squares optimization problem, and apply the nonlinear conjugate gradient method to solve the smoothing model. The algorithm is shown globally convergent. In addition, the simulation results not only suggest some nice smoothing functions, but also show that the proposed algorithm is competitive in view of relative error.

Original languageEnglish
Article number42
JournalCalcolo
Volume56
Issue number4
DOIs
Publication statusPublished - 2019 Dec 1
Externally publishedYes

    Fingerprint

Keywords

  • Compressive sensing
  • Conjugate gradient algorithm
  • l-norm regularization
  • Smoothing function

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

Cite this