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 journalArticlepeer-review

26 Scopus citations


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
Issue number11
StatePublished - Sep 20 2016


  • 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


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