| Image compression is the process of reducing the number of bits required to represent an image, while maintaining its visual quality. Typically, it is performed in two steps: density estimation, wherein training images are used to generate a probabilistic model of the source; and quantizer design, wherein the source model is used to design a quantizer that meets desired constraints on rate and distortion.; Unfortunately, training data are scarce, often inadequate to yield a good model of the source. Therefore, the quantizer may be based on an inaccurate source model. Indeed, when the quantizer is tested subsequently on real-world images, it is common to find its performance to be lower than expected.; It is our goal to avoid such surprises in the field. To this end, we model the source as a Gauss mixture (GM) and design an optimal classified vector quantizer (CVQ) for it. The claim is not that the source model is in fact a GM, but rather that it cannot hurt to assume so. More precisely, let the true source model be any distribution with the same class probabilities and the same per-class means and covariances as the GM model. Then, we claim that the CVQ will yield the same rate and distortion with the true source model as with the GM model. This robustness result is proved in the high-rate limit and is justified by extensive simulations at low rates.; Next, we consider Gaussian auto-regressive (AR) mixtures. AR models have been used extensively in linear predictive coding (LPC) of speech; here we consider 2-D extensions to images. We demonstrate the robustness result for AR mixtures using extensive simulations, and show that robustness conditions for AR mixtures are less stringent than those for GM models.; Simulation results show that vector quantization based on a GM model or an AR mixture model provides robust performance on out-of-training images. In addition, the scheme may be enhanced to perform supervised and unsupervised classification. The framework also provides pleasing connections with MAP classification, ML estimation, high-rate theory, Kullback-Leibler distance, LPC and CELP. |
