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Contourlet Filter Design Based on Chebyshev Best Uniform Approximation


The contourlet transform can deal effectively with images which have directional information such as contour and texture. In contrast to wavelets for which there exists many good filters, the contourlet filter design for image processing applications is still an ongoing work. Therefore, this paper presents an approach for designing the contourlet filter based on the Chebyshev best uniform approximation for achieving an efficient image denoising applications using hidden Markov tree models in the contourlet domain. Here, we design both the optimal 9/7 wavelet filter banks with rational coefficients and new pkva 12 filter. In this paper, the Laplacian pyramid followed by the direction filter banks decomposition in the contourlet transform using the two filter banks above and the image denoising applications in the contourlet hidden Markov tree model are implemented, respectively. The experimental results show that the denoising performance of the test image Zelda in terms of peak signal-to-noise ratio is improved by 0.33 dB than using CDF 9/7 filter banks with irrational coefficients on the JPEG2000 standard and standard pkva 12 filter, and visual effects are as good as compared with the research results of Duncan D.-Y. Po and Minh N. Do.

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Correspondence to Guoan Yang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yang, G., Fang, X., Jing, M. et al. Contourlet Filter Design Based on Chebyshev Best Uniform Approximation. EURASIP J. Adv. Signal Process. 2010, 398385 (2010).

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  • Pyramid
  • Rational Coefficient
  • Filter Bank
  • Uniform Approximation
  • Image Denoising