Affine Modeling for the Complexity of Vector Quantizers

We use a scalar function thetas to describe the complexity of data compression systems based on vector quantizers (VQs). This function is associated with the analog hardware implementation of a VQ, as done for example in focal-plane image compression systems. The rate and distortion of a VQ are represented by a Lagrangian cost function J. In this work we propose an affine model for the relationship between J and thetas, based on several VQ encoders performing the map R M rarr {1,2,..., K}. A discrete source is obtained by partitioning images into 4x4 pixel blocks and extracting M = 4 principal components from each block. To design entropy-constrained VQs (ECVQs), we use the Generalized Lloyd Algorithm. To design simple interpolative VQs (IVQs), we consider only the simplest encoder: a linear transformation, followed by a layer of M scalar quantizers in parallel - the K cells of M.M are defined by a set of thresholds {t I ,... ,t T }. The T thresholds are obtained from a non-linear unconstrained optimization method based on the Nelder-Mead algorithm.