Image restoration by minimizing zero norm of wavelet frame coefficients

Chenglong Bao, Bin Dong, Likun Hou, Zuowei Shen, Xiaoqun Zhang, Xue Zhang

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the ℓ0-norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka-łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of ℓ0-norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.

Original languageEnglish (US)
Article number115004
JournalInverse Problems
Volume32
Issue number11
DOIs
StatePublished - Sep 20 2016
Externally publishedYes

Fingerprint

Wavelet Frames
Image Restoration
Image reconstruction
Norm
Zero
Coefficient
Thresholding
Signal Reconstruction
Signal reconstruction
Linear Convergence
Local Minimizer
Line Search
Image Reconstruction
Computational efficiency
Computational Efficiency
Convergence Rate
Regularization
Numerical Experiment
Converge
Demonstrate

Keywords

  • iterative hard threshholding
  • local minimizer
  • wavelet frame
  • ℓ regularization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Cite this

Image restoration by minimizing zero norm of wavelet frame coefficients. / Bao, Chenglong; Dong, Bin; Hou, Likun; Shen, Zuowei; Zhang, Xiaoqun; Zhang, Xue.

In: Inverse Problems, Vol. 32, No. 11, 115004, 20.09.2016.

Research output: Contribution to journalArticle

Bao, Chenglong ; Dong, Bin ; Hou, Likun ; Shen, Zuowei ; Zhang, Xiaoqun ; Zhang, Xue. / Image restoration by minimizing zero norm of wavelet frame coefficients. In: Inverse Problems. 2016 ; Vol. 32, No. 11.
@article{9ec0a2a508ab4c79b0ce81e80f642f9c,
title = "Image restoration by minimizing zero norm of wavelet frame coefficients",
abstract = "In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the ℓ0-norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka-łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of ℓ0-norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.",
keywords = "iterative hard threshholding, local minimizer, wavelet frame, ℓ regularization",
author = "Chenglong Bao and Bin Dong and Likun Hou and Zuowei Shen and Xiaoqun Zhang and Xue Zhang",
year = "2016",
month = "9",
day = "20",
doi = "10.1088/0266-5611/32/11/115004",
language = "English (US)",
volume = "32",
journal = "Inverse Problems",
issn = "0266-5611",
publisher = "IOP Publishing Ltd.",
number = "11",

}

TY - JOUR

T1 - Image restoration by minimizing zero norm of wavelet frame coefficients

AU - Bao, Chenglong

AU - Dong, Bin

AU - Hou, Likun

AU - Shen, Zuowei

AU - Zhang, Xiaoqun

AU - Zhang, Xue

PY - 2016/9/20

Y1 - 2016/9/20

N2 - In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the ℓ0-norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka-łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of ℓ0-norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.

AB - In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the ℓ0-norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka-łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of ℓ0-norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.

KW - iterative hard threshholding

KW - local minimizer

KW - wavelet frame

KW - ℓ regularization

UR - http://www.scopus.com/inward/record.url?scp=85009212797&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009212797&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/32/11/115004

DO - 10.1088/0266-5611/32/11/115004

M3 - Article

VL - 32

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 11

M1 - 115004

ER -