A New Algorithm Framework for Image Inpainting in Transform Domain

Fang Li*, Tieyong Zeng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

10 Citations (Scopus)
23 Downloads (Pure)


In this paper, we focus on variational approaches for image inpainting in transform domain and propose two new algorithms, iterative coupled transform domain inpainting (ICTDI) and iterative decoupled transform domain inpainting. In the derivation of ICTDI, we use operator splitting and the quadratic penalty technique to get a new approximate problem of the basic model. By the alternating minimization method, the approximate problem can be decomposed as three relatively simple subproblems with closed-form solutions. However, ICTDI is not efficient when some adaptive regularization operator is used, such as the learned BM3D frame. To overcome this drawback, with some modifications, we decouple our framework into three relatively independent parts: denoising, linear combination in the transform domain, and linear combination in the image domain. Therefore, we can use any existing denoising method in the denoising step. We consider three choices for regularization operators in our approach: gradient operator, tight framelet transform, and learned BM3D frame. The numerical experiments and comparisons on various images demonstrate the effectiveness of the proposed methods. The convergence of the numerical algorithms is proved under some assumptions.

Original languageEnglish
Pages (from-to)24-51
Number of pages28
JournalSIAM Journal on Imaging Sciences
Issue number1
Publication statusPublished - 12 Jan 2016

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • BM3D frame
  • Image inpainting
  • Shrinkage
  • Transform domain


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