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Calculations based on high-resolution quantizations prove that the distortion rate D(R) of an image transform coding is proportional to 2/sup -2R/ when R is large enough. In wavelet and block cosine bases, we show that if R<1 bit/pixel, then D(R) varies like R/sup 1-2/spl gamma//, where /spl gamma/ remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. At low bit rates, we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors.
Mallat et al. (Wed,) studied this question.