A filter design strategy for binary field wavelet transform using the perpendicular constraint

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 multiresolution properties, three constraints are placed on the filters, namely the bandwidth, the perfect reconstruction and the vanishing moment constraints. While these constraints guarantee the existence of the inverse filters, their form is unconstrained and could be signal length dependent. In this paper, we propose to use the perpendicular constraint to relate the forward and inverse filters. With this constraint, it is shown that the form of the inverse filters remains unchanged after the up-sampling operation associated with the wavelet transform. We also explore an efficient implementation structure in the binary filters so as to save memory space and reduce the computational complexity. A detailed comparison with the lifting implementation in the real field wavelet transform is carried out. It is found that the computational complexity of the binary filter is significantly less than that of the real field wavelet kernel.