Multiplication-free vector quantization using L1 distortion measure and its variants

The authors first consider vector quantization that uses the L ₁ distortion measure for its implementation. The L ₁ distortion measure is very attractive from an implementational point of view, since no multiplication is required for computing the distortion measure. Unfortunately, the traditional Linde-Buzo-Gray method (1980) for designing the codebook for the L ₁ distortion measure can become extremely time-consuming, since it involves several computations of medians of very large arrays. The authors propose a gradient-based approach for codebook design that does not require any multiplications or median computations. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. By appropriate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. The authors apply the proposed techniques in predictive vector quantization of images and demonstrate the viability of multiplication-free predictive vector quantization of image data