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

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

doi:10.1007/s10092-019-0340-5

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

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

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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 language	English
Article number	42
Journal	Calcolo
Volume	56
Issue number	4
DOIs	https://doi.org/10.1007/s10092-019-0340-5
Publication status	Published - 2019 Dec 1

Keywords

Compressive sensing
Conjugate gradient algorithm
Smoothing function
l-norm regularization

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics

Access to Document

10.1007/s10092-019-0340-5

Cite this

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title = "Signal reconstruction by conjugate gradient algorithm based on smoothing l1 -norm",

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.",

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T1 - Signal reconstruction by conjugate gradient algorithm based on smoothing l1 -norm

AU - Wu, Caiying

AU - Zhan, Jiaming

AU - Lu, Yue

AU - Chen, Jein Shan

PY - 2019/12/1

Y1 - 2019/12/1

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AB - 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.

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