A binary wavelet decomposition of binary images
Swanson, M.D.
Tewfik, A.H.
Dept. of Electr. Eng., Minnesota Univ., Minneapolis, MN;
This paper appears in: Image Processing, IEEE Transactions on
Publication Date: Dec 1996
Volume: 5,
Issue: 12
On page(s): 1637-1650
ISSN: 1057-7149
References Cited: 25
CODEN: IIPRE4
INSPEC Accession Number: 5454406
Digital Object Identifier: 10.1109/83.544571
Current Version Published: 2002-08-06
Abstract
We construct a theory of binary wavelet decompositions of finite
binary images. The new binary wavelet transform uses simple module-2
operations. It shares many of the important characteristics of the real
wavelet transform. In particular, it yields an output similar to the
thresholded output of a real wavelet transform operating on the
underlying binary image. We begin by introducing a new binary field
transform to use as an alternative to the discrete Fourier transform
over GF(2). The corresponding concept of sequence spectra over GF(2) is
defined. Using this transform, a theory of binary wavelets is developed
in terms of two-band perfect reconstruction filter banks in GF(2). By
generalizing the corresponding real field constraints of bandwidth,
vanishing moments, and spectral content in the filters, we construct a
perfect reconstruction wavelet decomposition. We also demonstrate the
potential use of the binary wavelet decomposition in lossless image
coding
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