DATA COMPRESSION USING WAVELETS: ERROR, SMOOTHNESS, AND QUANTIZATION* Extended Abstract

Recently, a theory, developed by DeVore, Jawerth, and Popov, of nonlinear approximation by both orthogonal and nonorthogonal wavelets has been applied to problems in surface and image compression by DeVore, Jawerth, and Lucier. This theory relates precisely the norms in which the error is measured, the rate of decay in that error as the compression decreases, and the smoothness of the data. In addition, one can interpret the error incurred by the quantization of wavelet coefficients in terms of this theory. In this talk we give an overview of the previous results, and expand our argument, made earlier for image compression, that frequency-amplitude response curves that arise quite naturally in problems involving human visual and audio perception should be used to decide the quantization strategy for wavelet coefficients and the norm in which to measure the error in compressed data.