Multiplication free vector quantization using the L 1 distortion measure and its variants

Vector quantization is a very powerful technique for data compression and consequently, it has attracted a lot for attention lately. One major drawback associated with this approach is its extreme computational complexity. This paper fist 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 code book for the L1 distortion measure involves several computations of medians of very large arrays and can become very complex. We propose a gradient-based approach for codebook design that does not require any multiplications or median computations. Convergence of this method is proved rigorously under very mild conditions. Simulation examples comparting the performance of this technique with the LBG algorithm show that the gradient-based method, in spite of its simplicity, produces codebooks with average distortions that are comparable to the LBG algorithm. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. Once again, by appro[riate 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 predicitve vector quantization of images and demonstrate the viability of multiplication free predicitve vector quantization of image data.