Convergence of Newton's method for a minimization problem in impulse noise removal

Raymond H. CHAN*, Chung Wa HO, Mila NIKOLOVA

*Corresponding author for this work

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

22 Citations (Scopus)


Recently, two-phase schemes for removing salt-and-pepper and random-valued impulse noise are proposed in [6, 7]. The first phase uses decision-based median filters to locate those pixels which are likely to be corrupted by noise (noise candidates). In the second phase, these noise candidates are restored using a detail-preserving regularization method which allows edges and noise-free pixels to be preserved. As shown in [18], this phase is equivalent to solving a one-dimensional nonlinear equation for each noise candidate. One can solve these equations by using Newton's method. However, because of the edge-preserving term, the domain of convergence of Newton's method will be very narrow. In this paper, we determine the initial guesses for these equations such that Newton's method will always converge.

Original languageEnglish
Pages (from-to)168-177
Number of pages10
JournalJournal of Computational Mathematics
Issue number2
Publication statusPublished - Mar 2004
Externally publishedYes


  • Impulse noise denoising
  • Newton's method
  • Variational method


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