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Improving the compression rate versus L 1 error ratio in cell-average error control algorithms

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Abstract

Multiresolution representations of data are powerful tools in data compression. A common framework for applications is the cell-average setting. For a proper adaptation to singularities, it is interesting to develop nonlinear methods. Thus, one needs to control the stability of these representations. We introduce a generalization, depending on a parameter λ, of the classical cell-average error-control algorithms and we study the choice of the parameter to get the best relation quality vs. ratio of compression. It turns out that λ can be chosen nonlinearly and that for the L 1 norm we can get a significant improvement over the classical error-control algorithms.

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Authors and Affiliations

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

    Sergio Amat & J. Carlos Trillo

  2. Departamento de Matemáticas, Universidad de Alcalá de Henares, Madrid, Spain

    Juan Ruiz

Authors
  1. Sergio Amat
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  2. Juan Ruiz
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  3. J. Carlos Trillo
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Corresponding author

Correspondence to J. Carlos Trillo.

Additional information

Research supported in part by the project MTM2010-17508 and by the Seneca project 08662/PI/08.

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Amat, S., Ruiz, J. & Trillo, J.C. Improving the compression rate versus L 1 error ratio in cell-average error control algorithms. Numer Algor 67, 145–162 (2014). https://doi.org/10.1007/s11075-013-9780-1

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  • DOI: https://doi.org/10.1007/s11075-013-9780-1

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