Alternating direction method for image inpainting in wavelet domains

Raymond H. CHAN, Junfeng YANG, Xiaoming YUAN*

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

86 Citations (Scopus)


Image inpainting in wavelet domains refers to the recovery of an image from incomplete and/or inaccurate wavelet coefficients. To reconstruct the image, total variation (TV) models have been widely used in the literature, and they produce high-quality reconstructed images. In this paper, we consider an unconstrained, TV-regularized, ℓ2-data-fitting model to recover the image. The model is solved by the alternating direction method (ADM). At each iteration, the ADM needs to solve three subproblems, all of which have closed-form solutions. The per-iteration computational cost of the ADM is dominated by two Fourier transforms and two wavelet transforms, all of which admit fast computation. Convergence of the ADM iterative scheme is readily obtained. We also discuss extensions of this ADM scheme to solving two closely related constrained models. We present numerical results to show the efficiency and stability of the ADM for solving wavelet domain image inpainting problems. Numerical results comparing the ADM with some recent algorithms are also reported.

Original languageEnglish
Pages (from-to)807-826
Number of pages20
JournalSIAM Journal on Imaging Sciences
Issue number3
Publication statusPublished - Jan 2011
Externally publishedYes


  • Alternating direction method
  • Augmented lagrangian method
  • Fast fourier transform
  • Fast wavelet transform
  • Inpainting
  • Total variation
  • Wavelet


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