On the importance of combining wavelet-based nonlinear approximation with coding strategies

• Published in: IEEE transactions on information theory Vol. 48; no. 7; pp. 1895 - 1921
• Main Authors: Cohen, A., Daubechies, I., Guleryuz, O.G., Orchard, M.T.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2002; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Approximation methods; Compressing; Data compression; Image coding; Mathematical analysis; Mathematical models; Nonlinearity; Rate distortion theory; Stochastic processes; Strategy; Transform coding; Transforms; Wavelet transforms

This paper provides a mathematical analysis of transform compression in its relationship to linear and nonlinear approximation theory. Contrasting linear and nonlinear approximation spaces, we show that there are interesting classes of functions/random processes which are much more compactly represe...