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   -> Volume 6, Issue 3


Preprint: Understanding Wavelet Image Transform Codes
 
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Stephane Mallat (mallat@cmapx.polytechnique.fr)
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PostPosted: Thu Feb 13, 1997 11:08 am    
Subject: Preprint: Understanding Wavelet Image Transform Codes
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#1 Preprint: Understanding Wavelet Image Transform Codes

Understanding Wavelet Image Transform Codes

Stephane Mallat and Frederic Falzon

Ecole Polytechnique, CMAP, 91128 Palaiseau Cedex
INRIA, Projet Pastis, Sophia Antipolis

Abstract
The high resolution quantization hypothesis
is not appropriate to evaluate the distortion-rate
of image transform codes in orthogonal bases.
It is shown that the compression performance depends mostly
on the precision of non-linear signal approximations with few non-zero bases
vectors. At low bit rates, for a number of bit per pixel R
that is below 1, the distortion D(R) decays like $R^{-C}$ instead
of $2^{-2 R}$ as predicted by the high resolution transform
code theory. The constant C is typically of the order
of 1 for natural images decomposed in a wavelet basis,
or in a cosine basis for JPEG. The improved performance of embedded
codes in wavelet bases is also explained.

The paper is in the compressed file pub/Mallat/ImageCode.ps.gz that
can be retrieved by anonymous ftp at the address: 129.104.4.100

ftp://129.104.4.100/pub/Mallat/ImageCode.ps.gz
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