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

摘要

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.