Wavelet approximation methods in image and signal compression

The material in this paper comes from various conferences given by the authors. We start with a brief survey of harmonic analysis methods in linear and non-linear approximation related to signal compression. Special emphasis is made on wavelet-based methods and some of the mathematical theory of wavelets behind them. We also present recent results of the authors concerning nonlinear approximation in sequence spaces and the validity of Jackson and Bernstein inequalities in general smoothness spaces.

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