Orthonormal integer block transforms for lossless coding: design and performance analysis

In this paper a general framework for N-point, where N=2 with d ∈ Z and d > 0, orthonormal block transforms that map integers to integers using the lifting scheme is presented. The design of the Discrete Cosine Transform (DCT) that maps integers to integers (I2I-DCT), the Discrete Sine Transform that maps integers to integers (I2I-DST) and the Walsh Hadamard Transform that maps integer to integers (I2I-WHT) is presented. The main significance of this design is that the orthonormal property of the transforms is maintained by proper normalisation while preserving the integer to integer mapping and perfect reconstruction. This makes these transforms usable in both lossless and lossy image coding, especially in scalable lossless coding. The coding performance of these transforms is evaluated in lossless image coding and lossless video coding applications.