Data compression using wavelets: error, smoothness and quantization

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. 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. This overview of the previous results expands the 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