Lattice vector quantization for image coding

The authors investigate the application of several lattice vector quantizers, namely D_N for N⩽8, Z ^N for N⩽16, and E₈, to the quantization of 2-D DCT (discrete cosine transform) coefficients at rates less than 1.0 bit/pixel. They use 16×16 blocks for the DCT and consider a variety of 256×156 monochrome images. Methods for scaling and truncating the lattices to obtain the desired bit rate are described, and techniques for encoding any vectors that fall outside the design radius are given. The lattice vector quantizers are compared among themselves and to an LBG (Y. Linde, A. Buzo, and R.M. Gray, IEEE Trans. Commun., vol.COM-28, p.84-95, Jan. 1980) training mode vector quantizer. The lattice quantizers of a given dimension N achieve approximately the same SNR and equivalent image quality; thus the Z^N lattice is preferred because of its extremely simple encoding algorithm. For some images the Z¹⁶ lattice outperforms the simplified LBG vector quantizer in both SNR and reconstructed image quality, and it requires an order of magnitude less encoding time