Gersho's bounds on the asymptotic performance of vector quantizers are valid for vector distortions which are powers of the Euclidean norm. Yamada, Tazaki and Gray generalized the results to distortion measures that are increasing functions of the norm of their argument. In both cases, the distortion is uniquely determined by the vector quantization error, i.e., the Euclidean difference between the original vector and the codeword into which it is quantized. We generalize these asymptotic bounds to input-weighted quadratic distortion measures, a class of distortion measure often used for perceptually meaningful distortion. The generalization involves a more rigorous derivation of a fixed rate result of Gardner and Rao and a new result for variable rate codes. We also consider 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 dB is shown...

The use of a compander (compressor-expander) in conjuction with scalar uniform high-resolution quantization, so as to obtain an overall effect of an improved nonuniform quantization, has been widespread for many years and embedded in standards of digitization and compression of audio waveforms (-law in the U.S., and A-law in Europe). However, there is almost no reported work on its usefulness in still image and motion picture coding. In this work, we are making an attempt to embed companders in the JPEG algoirithm and our results show considerable improvement (10-25%) in compression ratio for large PSNR's. Strictly speaking, the new scheme is not standard compliant. However, with suitable preperocessing and postprocessing it can be implemented in a standard compliant manner. Also, the results of this research might be useful for the quantization part of future standards such as JPEG 2000. Keywords: image compression, JPEG, companding. N. Merhav is with Department of Electri...