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On a nonlinear mean and its application to image compression using multiresolution schemes

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Abstract

This paper is devoted to the compression of colour images using a new nonlinear cell-average multiresolution scheme. The aim is to obtain similar compression properties as linear multiresolution schemes but eliminating the classical Gibbs phenomenon of this type of reconstructions near the edges. The algorithm is based on a nonlinear reconstruction operator (using a nonlinear trigonometric mean). The new reconstruction is third-order accurate in smooth regions and adapted to the presence of discontinuities. The data used are always centred with optimal support. Some theoretical properties of this scheme are analysed (order of approximation, convergence, elimination of Gibbs effect and stability).

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Authors and Affiliations

  1. Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, Spain

    S. Amat & J. C. Trillo

  2. Ecole Superieure de Mecanique de Marseille, Laboratoire d’Analyse Topologie et Probabilites, Marseille, France

    J. Liandrat

  3. Departamento de Física y Matemáticas, Universidad de Alcalá de Henares, Madrid, Spain

    J. Ruiz

Authors
  1. S. Amat
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  2. J. Liandrat
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  3. J. Ruiz
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  4. J. C. Trillo
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Corresponding author

Correspondence to J. Ruiz.

Additional information

Research supported by MICINN-FEDER MTM2010-17508 (Spain) and by 08662/PI/08 (Murcia).

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Amat, S., Liandrat, J., Ruiz, J. et al. On a nonlinear mean and its application to image compression using multiresolution schemes. Numer Algor 71, 729–752 (2016). https://doi.org/10.1007/s11075-015-0019-1

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  • DOI: https://doi.org/10.1007/s11075-015-0019-1

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