Invertible Integer Lie Group Transforms

Abstract

Invertible integer transforms are essential for lossless source encoding. Using lifting schemes, we develop a new family of invertible integer transforms based on discrete generalized cosine transforms. The discrete generalized cosine transforms that arise in connection with compact semi-simple Lie groups of rank 2, are orthogonal over a fundamental region and have recently attracted more attention in digital image processing. Since these integer transforms are invertible, they have potential applications in lossless image compression and encryption.