Analysis of low bit rate image transform coding

Author

Mallat, Stéphane ; Falzon, Frederic

Author_Institution

Dept. of Appl. Math., New York Univ., NY, USA

Volume

46

Issue

4

fYear

1998

fDate

4/1/1998 12:00:00 AM

Firstpage

1027

Lastpage

1042

Abstract

Calculations based on high-resolution quantizations prove that the distortion rate D(R¯) of an image transform coding is proportional to 2^-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¯^1-2γ, where γ 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

Keywords

data compression; image coding; image resolution; quantisation (signal); rate distortion theory; transform coding; wavelet transforms; block cosine bases; compression performance; distortion rate; embedded coding; high-resolution quantization; image approximation; low bit rate image transform coding; natural images; nonzero vectors; orthonormal basis; wavelet bases; Bit rate; Entropy; Image analysis; Image coding; Pixel; Quantization; Rate distortion theory; Transform coding; Wavelet analysis; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.668554

Filename

668554