Wavelet decomposition of binary finite images

Constructs a theory of wavelet decompositions of binary images. The construction defines binary valued wavelets and scaling functions and their associated spectral properties. The authors begin by introducing a new binary field transform and the corresponding concept of sequence spectra over GF(2). Using this transform, a theory of binary wavelets is then developed in terms of 2-band perfect reconstruction filter banks. By generalizing the corresponding real field constraints of bandwidth, vanishing moments, and spectral content in the filters, a perfect reconstruction wavelet decomposition is created. An example to illustrate the potential use for compression applications is included.<>