Multiplication-free vector quantization using the L l distortion measure and its variants

Vector quantization is a very powerful technique for data compression and consequently, it has attracted a lot of attention lately. One major drawback associated with this approach is its extreme computational complexity. This paper first considers vector quantization that uses the L1 distortion measure for its implementation. The L1 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 (LBG) method for designing the codebook for the L1 distortion measure can become extremely time-consuming, since it involves several computations of medians of very large arrays. We 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. Once again, by appropriate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. Finally, we apply our techniques in predictive vector quantization of images and demonstrate the viability of multiplication-free predictive vector quantization of image data.