title: A binary wavelet decomposition of binary images.
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.
authors.affiliation: Dept. of Electr. Eng., Minnesota Univ., Minneapolis, MN.
authors.forename: M D
authors.initials: MD
authors.lastname: Swanson
authors.forename: A H
authors.initials: AH
authors.lastname: Tewfik