WAVELET APPROXIMATION METHODS IN IMAGE AND SIGNAL COMPRESSION

Abstract. 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 non-linear approximation in sequence spaces and the validity of Jackson and Bernstein inequalities in general smoothness spaces. 1