A Comparison of the Z, E8, and Leech Lattices for Image Subband Quantization

Lattice vector quantization schemes offer high coding e f i c i ency without t he burden associated with generating and searching a codebook. T h e dis tort ion associated with a given lattice is of ten expressed i n t e r m s of the G number, which is a measure of the m e a n square error per dimension generated by quantization of a u n i f o r m source. Subband image coef ic ients , however, are best modeled by a generalized Gaussian, leading t o dis tort ion characteristics that are quite di f ferent f r o m those encountered f o r un i form, Laplacian, o r Gaussian sources. We present here the dis tort ion associated with 2, E8, and Leech lattice quantization f o r coding of generalized Gauss ian sources, and show that f o r low bit rates the Z lattice offers both the best performance and the lowest implementat ional complexity.