Issues of filter design for binary wavelet transform

Wavelet decomposition has recently been generalized to binary field in which the arithmetic is performed wholly in GF(2). In order to maintain an invertible binary wavelet transform with desirable multiresolution properties, the bandwidth, the perfect reconstruction and the vanishing moment constraints are placed on the binary filters. While they guarantee an invertible transform, the transform becomes non-orthogonal and non-biorthogonal in which the inverse filters could be signal length-dependent. We propose to apply the perpendicular constraint on the binary filters to make them length independent. A filter design strategy is outlined in which a filter design for a length of eight is given. We also propose an efficient implementation structure for the binary filters that saves memory space and reduces the computational complexity.