Analysis of simultaneous inpainting and geometric separation based on sparse decomposition

Van Tiep Do, Ron Levie, Gitta Kutyniok

Research output: Contribution to journalArticlepeer-review


Natural images are often the superposition of various parts of different geometric characteristics. For instance, an image might be a mixture of cartoon and texture structures. In addition, images are often given with missing data. In this paper, we develop a method for simultaneously decomposing an image to its two underlying parts and inpainting the missing data. Our separation-inpainting method is based on an l1 minimization approach, using two dictionaries, each sparsifying one of the image parts but not the other. We introduce a comprehensive convergence analysis of our method, in a general setting, utilizing the concepts of joint concentration, clustered sparsity, and cluster coherence. As the main application of our theory, we consider the problem of separating and inpainting an image to a cartoon and texture parts.

Original languageEnglish
Pages (from-to)303-352
Number of pages50
JournalAnalysis and Applications
Issue number2
StatePublished - 1 Mar 2022
Externally publishedYes


  • Image separation
  • cartoon
  • cluster coherence
  • cluster sparsity
  • inpainting
  • l 1 minimization
  • l(1) minimization
  • shearlets
  • sparsity
  • texture

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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