Circuits, Systems, and Signal Processing

, Volume 32, Issue 4, pp 1725–1744 | Cite as

Design of Biorthogonal Filter Banks Using a Multi-objective Genetic Algorithm for an Image Coding Scheme

  • Abdelkader Boukhobza
  • Abdennacer Bounoua
  • Abdelmalik Taleb-Ahmed
  • Nasreddine Taleb
Article
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Revised:

Abstract

In this paper, we present an optimization method based on a multi-objective Genetic Algorithm (GA) for the design of linear phase filter banks for an image coding scheme. To be effective, the filter banks should satisfy a number of desirable criteria related to such a scheme. Instead of imposing the entire PR condition as in conventional designs, we introduce flexibility in the design by relaxing the Perfect Reconstruction (PR) condition and defining a PR violation measure as an objective criterion to maintain near perfect reconstruction (N-PR) filter banks. Particularly in this work, the designed filter banks are near-orthogonal. This has been made possible by minimizing the deviation from the orthogonality in the optimization process. The optimization problem is formulated as a constrained multi-objective, and a modified Nondominated Sorting Genetic Algorithm NSGAII is proposed in this work to find the Pareto optimal solutions that achieve the best compromise between the different objective criteria. The experimental results show that the filter banks designed with the proposed method outperform significantly the 9/7 filter bank of JPEG2000 in most cases. Furthermore, the filter banks are near orthogonal. This is very helpful, especially where embedded coding is required.

Keywords

Filter bank design Wavelet Image coding Multi-objective optimization Genetic algorithm 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Abdelkader Boukhobza
    • 1
  • Abdennacer Bounoua
    • 1
  • Abdelmalik Taleb-Ahmed
    • 2
  • Nasreddine Taleb
    • 1
  1. 1.RCAM LaboratoryDjillali Liabes University of Sidi Bel-AbbesSidi Bel-AbbesAlgeria
  2. 2.LAMIH UMR CNRS 8201 UVHCValenciennes Cedex 9France

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