Asymptotic performance of vector quantizers with a perceptual distortion measure

Gersho's bounds on the asymptotic performance of vector quantizers are vali d for vector distortions which are powers of the Euclidean norm. Yamada, Ta zaki, and Gray generalized the results to distortion measures that are incr easing functions of the norm of their argument. In both cases, the distorti on is uniquely determined by the vector quantization error, i.e., the Eucli dean difference between the original vector and the codeword into which it is quantized, We generalize these asymptotic bounds to input-weighted quadr atic distortion measures and measures that are approximately output-weighte d-quadratic when the distortion is small, a class of distortion measures of ten claimed to be perceptually meaningful, An approximation of the asymptot ic distortion based on Gersho's conjecture is derived as well. We also cons ider the problem of source mismatch, where the quantizer is designed using a probability density different from the true source density. The resulting asymptotic performance in terms of distortion increase in decibels is show n to be linear in the relative entropy between the true and estimated proba bility densities.