Asymptotically Optimal Distribution Preserving Quantization for Stationary Gaussian Processes
(English)Manuscript (preprint) (Other academic)
Distribution preserving quantization (DPQ) has been proposed as a lossy coding tool that yieldssuperior quality over conventional quantization, when applied to perceptually relevant signals. DPQ aimsat the optimal rate-distortion trade-off, subject to preserving the source probability distribution. In thisarticle we investigate the optimal DPQ for stationary Gaussian processes and the mean squared error(MSE). A lower bound on the optimal performance is derived. A quantization scheme is proposed andproven to asymptotically reach the lower bound. For the sake of applicability, the scheme is simplified,though without affecting its asymptotic rate-distortion behavior. While this simplification sacrifices theexact preservation of the probability distribution, it strictly preserves the power spectral density (PSD) ofthe source. This leads to the consideration of another type of quantization: PSD preserving quantization(PSD-PQ). It is shown that the optimal rate-distortion trade-off for PSD-PQ equals that for DPQ, althoughit has a weaker constraint. The proposed quantizer is applied to audio coding and compared to aconventional method that is optimized for a rate-distortion trade-off without the distribution preservingconstraint. The results demonstrate that the new method leads to better perceptual quality.
Distribution preserving quantization (DPQ), Rate-distortion function (RDF), Entropy coded dithered quantization (ECDQ), Differential pulse-code modulation (DPCM), Perceptual audio coding
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-38517OAI: oai:DiVA.org:kth-38517DiVA: diva2:437192
QC 201108292011-08-292011-08-262011-08-29Bibliographically approved