Approximation BFGS methods for nonlinear image restoration

Lin Zhang Lu, Kwok Po NG*, Fu Rong Lin

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)


We consider the iterative solution of unconstrained minimization problems arising from nonlinear image restoration. Our approach is based on a novel generalized BFGS method for such large-scale image restoration minimization problems. The complexity per step of the method is of O (n log n) operations and only O (n) memory allocations are required, where n is the number of image pixels. Based on the results given in [Carmine Di Fiore, Stefano Fanelli, Filomena Lepore, Paolo Zellini, Matrix algebras in quasi-Newton methods for unconstrained minimization, Numer. Math. 94 (2003) 479-500], we show that the method is globally convergent for our nonlinear image restoration problems. Experimental results are presented to illustrate the effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)84-91
Number of pages8
JournalJournal of Computational and Applied Mathematics
Issue number1
Publication statusPublished - 1 Apr 2009

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Nonlinear image restoration
  • Optimization
  • Regularization


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