Design of lossless block transforms and filter banks for image coding

Lossless block transforms and filter banks that map integers to integers are important for unified lossless and lossy image coding systems. In this paper, we present simple yet effective methods for designing lossless versions of block transforms and FIR filter banks. First, an N-point lossless transform and a lossless interpolative prediction are introduced. Next, we demonstrate that filter banks can be decomposed into 2-point transforms or interpolative predictions. Lastly, lossless versions of block transforms and filter banks are obtained by replacing every constituent module by the corresponding lossless version. Lossless versions of 8-point discrete cosine transform (DCT), 8-point Walsh-Hadamard transform (WHT) and several filter banks are designed and their lossless compression performance is evaluated.