Iterative regularized least-mean mixed-norm image restoration

Min Cheol Hong, Tania Stathaki, Aggelos K. Katsaggelos

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We develop a regularized mixed-norm image restoration algorithm to deal with various types of noise. A mixed-norm functional is introduced, which combines the least mean square (LMS) and the least mean fourth (LMF) functionals, as well as a smoothing functional. Two regularization parameters are introduced: one to determine the relative importance of the LMS and LMF functionals, which is a function of the kurtosis, and another to determine the relative importance of the smoothing functional. The two parameters are chosen in such a way that the proposed functional is convex, so that a unique minimizer exists. An iterative algorithm is utilized for obtaining the solution, and its convergence is analyzed. The novelty of the proposed algorithm is that no knowledge of the noise distribution is required, and the relative contributions of the LMS, the LMF, and the smoothing functionals are adjusted based on the partially restored image. Experimental results demonstrate the effectiveness of the proposed algorithm.

Original languageEnglish (US)
Pages (from-to)2515-2524
Number of pages10
JournalOptical Engineering
Issue number10
StatePublished - Oct 2002


  • Convex
  • Kurtosis
  • LMF
  • LMS
  • Mixed-norm functional

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering(all)


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