The design of linear binary wavelet transforms and their application to binary image compression

This papers investigates linear binary wavelet transforms: convolutions of finite sequences of binary numbers with binary filters. These wavelets can be implemented using binary arithmetic only, which makes calculations simple and fast in practice. The paper presents some results that characterize binary wavelets completely for signal lengths that are powers of two. In addition, a design strategy is proposed that produces forward filters and inverse filters simultaneously by subsequently doubling the lengths of the filters. The paper concludes by investigating the effect of filter length on the compression of binary images.