New approximations of the total variation and filters in imaging

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21 Scopus citations


In this paper I present several results concerning the approximation of the BV-norm by non-local functionals. Some of these functionals are convex, others are non-convex. The mode of convergence introduces mysterious novelties and numerous problems remain open. The original motivation comes from Image Processing.

Original languageEnglish (US)
Pages (from-to)223-240
Number of pages18
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Issue number2
StatePublished - 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Bounded variation
  • Non-convex functional
  • Non-local functional
  • Total variation
  • Γ-convergence


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