A pyramidal scheme for lattice vector quantization of wavelet transform coefficients applied to image coding

The image coding scheme involves two steps: biorthogonal wavelet transform of the image and pyramidal lattice vector quantization of wavelet coefficients. In order to obtain a compromise between minimum distortion and bit rate, one must truncate and scale the lattice suitably. To meet this goal, one needs to know how many lattice points lie within the truncated area. The case of Laplacian sources where surfaces of equal probability are spheres for the L₁ metric (pyramids) for arbitrary lattices is investigated. Explicit generating functions for the codebook sizes of the most useful lattices are given