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

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 represented by wavelet-based nonlinear approximation. These classes include locally smooth signals that have singularities, and provide a model for many signals encountered in practice, in particular for images. However, we also show that nonlinear approximation results do not always translate to efficient compression strategies in a rate-distortion sense. Based on this observation, we construct compression techniques and formulate the family of functions/stochastic processes for which they provide efficient descriptions in a rate-distortion sense. We show that this family invariably leads to Besov spaces, yielding a natural relationship among Besov smoothness, linear/nonlinear approximation order,...

• Type: Journal
• Year: 2002
• Where: TIT
• Authors: Albert Cohen, Ingrid Daubechies, Onur G. Guleryuz, Michael T. Orchard
• Keywords: Nonlinear Approximation, Rate-distortion Sense, TIT 2002, Wavelet-based Nonlinear Approximation