Improving the compression rate versus L <sup>1</sup> error ratio in cell-average error control algorithms

Numerical Algorithms
  • Volumen: 67
  • Número: 1
  • Fecha: 01 September 2014
  • Páginas: 145-162
  • ISSN: 15729265 10171398
  • Source Type: Journal
  • DOI: 10.1007/s11075-013-9780-1
  • Publisher: Springer New York
© 2013, Springer Science+Business Media New York.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 ¿, 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 ¿ can be chosen nonlinearly and that for the L1 norm we can get a significant improvement over the classical error-control algorithms.

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