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Asymptotically Optimal Distribution Preserving Quantization for Stationary Gaussian Processes
KTH, School of Electrical Engineering (EES), Sound and Image Processing.
INRIA (Centre de Recherche Rennes Bretagne Atlantique) and IRISA (CNRS UMR 6074). (METISS Research Group)
KTH, School of Electrical Engineering (EES), Sound and Image Processing.
KTH, School of Electrical Engineering (EES), Sound and Image Processing.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keyword [en]
Distribution preserving quantization (DPQ), Rate-distortion function (RDF), Entropy coded dithered quantization (ECDQ), Differential pulse-code modulation (DPCM), Perceptual audio coding
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-38517OAI: oai:DiVA.org:kth-38517DiVA: diva2:437192
Note
QC 20110829Available from: 2011-08-29 Created: 2011-08-26 Last updated: 2011-08-29Bibliographically approved
In thesis
1. Distribution Preserving Quantization
Open this publication in new window or tab >>Distribution Preserving Quantization
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In the lossy coding of perceptually relevant signals, such as sound and images, the ultimate goal is to achieve good perceived quality of the reconstructed signal, under a constraint on the bit-rate. Conventional methodologies focus either on a rate-distortion optimization or on the preservation of signal features. Technologies resulting from these two perspectives are efficient only for high-rate or low-rate scenarios. In this dissertation, a new objective is proposed: to seek the optimal rate-distortion trade-off under a constraint that statistical properties of the reconstruction are similar to those of the source.

The new objective leads to a new quantization concept: distribution preserving quantization (DPQ). DPQ preserves the probability distribution of the source by stochastically switching among an ensemble of quantizers. At low rates, DPQ exhibits a synthesis nature, resembling existing coding methods that preserve signal features. Compared with rate-distortion optimized quantization, DPQ yields some rate-distortion performance for perceptual benefits.

The rate-distortion optimization for DPQ facilitates mathematical analysis. The dissertation defines a distribution preserving rate-distortion function (DP-RDF), which serves as a lower bound on the rate of any DPQ method for a given distortion. For a large range of sources and distortion measures, the DP-RDF approaches the classic rate-distortion function with increasing rate. This suggests that, at high rates, an optimal DPQ can approach conventional quantization in terms of rate-distortion characteristics.

After verifying the perceptual advantages of DPQ with a relatively simple realization, this dissertation focuses on a method called transformation-based DPQ, which is based on dithered quantization and a non-linear transformation. Asymptotically, with increasing dimensionality, a transformation-based DPQ achieves the DP-RDF for i.i.d. Gaussian sources and the mean squared error (MSE).

This dissertation further proposes a DPQ scheme that asymptotically achieves the DP-RDF for stationary Gaussian processes and the MSE. For practical applications, this scheme can be reduced to dithered quantization with pre- and post-filtering. The simplified scheme preserves the power spectral density (PSD) of the source.

The use of dithered quantization and non-linear transformations to construct DPQ is extended to multiple description coding, which leads to a multiple description DPQ (MD-DPQ) scheme. MD-DPQ preserves the source probability distribution for any packet loss scenario.

The proposed schemes generally require efficient entropy coding. The dissertation also includes an entropy coding algorithm for lossy coding systems, which is referred to as sequential entropy coding of quantization indices with update recursion on probability (SECURE).

The proposed lossy coding methods were subjected to evaluations in the context of audio coding. The experimental results confirm the benefits of the methods and, therewith, the effectiveness of the proposed new lossy coding objective.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. xiii, 69 p.
Series
Trita-EE, ISSN 1653-5146 ; 2011:55
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-38482 (URN)978-91-7501-075-5 (ISBN)
Public defence
2011-09-16, Salongen, Osquarsbacke 31, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20110829Available from: 2011-08-29 Created: 2011-08-26 Last updated: 2011-08-29Bibliographically approved

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