Image restoration using total variation with overlapping group sparsity

Jun Liu, Ting Zhu Huang, Ivan Selesnick, Xiao Guang Lv, Po Yu Chen

Research output: Contribution to journalArticle

Abstract

Image restoration is one of the most fundamental issues in imaging science. Total variation regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase artifacts. In this work we extend the total variation with overlapping group sparsity, which we previously developed for one dimension signal processing, to image restoration. A convex cost function is given and an efficient algorithm is proposed for solving the corresponding minimization problem. In the experiments, we compare our method with several state-of-the-art methods. The results illustrate the efficiency and effectiveness of the proposed method in terms of PSNR and computing time.

Original languageEnglish (US)
Pages (from-to)232-246
Number of pages15
JournalInformation Sciences
Volume295
DOIs
StatePublished - Feb 20 2015

Fingerprint

Image Restoration
Total Variation
Image reconstruction
Sparsity
Overlapping
Total Variation Regularization
Cost functions
Minimization Problem
One Dimension
Convex function
Cost Function
Signal Processing
Signal processing
Efficient Algorithms
Imaging
Imaging techniques
Computing
Experiment
Image restoration
Experiments

Keywords

  • ADMM
  • Convex optimization
  • Image restoration
  • MM
  • Overlapping group sparsity
  • Total variation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Software
  • Computer Science Applications
  • Information Systems and Management
  • Artificial Intelligence

Cite this

Image restoration using total variation with overlapping group sparsity. / Liu, Jun; Huang, Ting Zhu; Selesnick, Ivan; Lv, Xiao Guang; Chen, Po Yu.

In: Information Sciences, Vol. 295, 20.02.2015, p. 232-246.

Research output: Contribution to journalArticle

Liu, Jun ; Huang, Ting Zhu ; Selesnick, Ivan ; Lv, Xiao Guang ; Chen, Po Yu. / Image restoration using total variation with overlapping group sparsity. In: Information Sciences. 2015 ; Vol. 295. pp. 232-246.
@article{7d18fff585194e0880220cf576d00598,
title = "Image restoration using total variation with overlapping group sparsity",
abstract = "Image restoration is one of the most fundamental issues in imaging science. Total variation regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase artifacts. In this work we extend the total variation with overlapping group sparsity, which we previously developed for one dimension signal processing, to image restoration. A convex cost function is given and an efficient algorithm is proposed for solving the corresponding minimization problem. In the experiments, we compare our method with several state-of-the-art methods. The results illustrate the efficiency and effectiveness of the proposed method in terms of PSNR and computing time.",
keywords = "ADMM, Convex optimization, Image restoration, MM, Overlapping group sparsity, Total variation",
author = "Jun Liu and Huang, {Ting Zhu} and Ivan Selesnick and Lv, {Xiao Guang} and Chen, {Po Yu}",
year = "2015",
month = "2",
day = "20",
doi = "10.1016/j.ins.2014.10.041",
language = "English (US)",
volume = "295",
pages = "232--246",
journal = "Information Sciences",
issn = "0020-0255",
publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Image restoration using total variation with overlapping group sparsity

AU - Liu, Jun

AU - Huang, Ting Zhu

AU - Selesnick, Ivan

AU - Lv, Xiao Guang

AU - Chen, Po Yu

PY - 2015/2/20

Y1 - 2015/2/20

N2 - Image restoration is one of the most fundamental issues in imaging science. Total variation regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase artifacts. In this work we extend the total variation with overlapping group sparsity, which we previously developed for one dimension signal processing, to image restoration. A convex cost function is given and an efficient algorithm is proposed for solving the corresponding minimization problem. In the experiments, we compare our method with several state-of-the-art methods. The results illustrate the efficiency and effectiveness of the proposed method in terms of PSNR and computing time.

AB - Image restoration is one of the most fundamental issues in imaging science. Total variation regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase artifacts. In this work we extend the total variation with overlapping group sparsity, which we previously developed for one dimension signal processing, to image restoration. A convex cost function is given and an efficient algorithm is proposed for solving the corresponding minimization problem. In the experiments, we compare our method with several state-of-the-art methods. The results illustrate the efficiency and effectiveness of the proposed method in terms of PSNR and computing time.

KW - ADMM

KW - Convex optimization

KW - Image restoration

KW - MM

KW - Overlapping group sparsity

KW - Total variation

UR - http://www.scopus.com/inward/record.url?scp=84961287812&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961287812&partnerID=8YFLogxK

U2 - 10.1016/j.ins.2014.10.041

DO - 10.1016/j.ins.2014.10.041

M3 - Article

VL - 295

SP - 232

EP - 246

JO - Information Sciences

JF - Information Sciences

SN - 0020-0255

ER -