Nonlinear binary wavelet transforms and their application to binary image compression

Most research on wavelet transforms of binary signals and images has been concentrated on linear transforms. This paper proposes a binary wavelet transform scheme that does not depend on the field structure of binary numbers and includes nonlinear transforms. As a result, the number of binary wavelet transforms increases drastically. It is demonstrated that the increased freedom in choosing a particular transform can be useful in binary image compression. Nonlinear transforms reduce the empirical entropy of the test images substantially better than linear transforms.