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Distribution Preserving Quantization
KTH, School of Electrical Engineering (EES). (Sound and Image Processing)
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: urn:nbn:se:kth:diva-38482ISBN: 978-91-7501-075-5 (print)OAI: oai:DiVA.org:kth-38482DiVA: diva2:437204
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
List of papers
1. Quantization with Constrained Relative Entropy and Its Application to Audio Coding
Open this publication in new window or tab >>Quantization with Constrained Relative Entropy and Its Application to Audio Coding
2009 (English)In: 127th Audio Engineering Society Convention 2009, 2009, 401-408 p.Conference paper, Published paper (Refereed)
Abstract [en]

Conventional quantization distorts the probability density of the source. In scenarios such as low bit rate audio coding, this leads to perceived distortion that is not well characterized by commonly used distortion criteria. We propose the relative entropy between the probability densities of the original and reconstructed signals as an additional fidelity measure. Quantization with a constraint on relative entropy ensures that the probability density of the signal is preserved to a controllable extent. When it is included in an audio coder, the new quantization facilitates a continuous transition between the underlying concepts of the vocoder, the bandwidth extension, and a rate-distortion optimized coder. Experiments confirm the effectiveness of the new quantization scheme.

National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-38538 (URN)2-s2.0-84866034529 (Scopus ID)978-161567712-2 (ISBN)
Conference
127th Audio Engineering Society Convention 2009; New York, NY; United States; 9 October 2009 through 12 October 2009
Note

QC 20110829

Available from: 2011-08-29 Created: 2011-08-26 Last updated: 2014-09-23Bibliographically approved
2. Distribution Preserving Quantization With Dithering and Transformation
Open this publication in new window or tab >>Distribution Preserving Quantization With Dithering and Transformation
2010 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 17, no 12, 1014-1017 p.Article in journal (Refereed) Published
Abstract [en]

A new quantization scheme that preserves the probability distribution of the source signal is presented. The distribution preserving quantization (DPQ) achieves the optimal trade-off between mean square error and bit rate asymptotically. It provides a continuum ranging from rate-distortion optimal signal quantization to parametric coding. The method can be used as a core component for scalable coding. Its efficacy is illustrated by applying the scheme to audio coding.

Keyword
Distribution preserving quantization, perceptual coding, scalable coding
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-27376 (URN)10.1109/LSP.2010.2087749 (DOI)000283981300001 ()2-s2.0-78149459675 (Scopus ID)
Note
QC 20101213Available from: 2010-12-13 Created: 2010-12-13 Last updated: 2017-12-11Bibliographically approved
3. On Distribution Preserving Quantization
Open this publication in new window or tab >>On Distribution Preserving Quantization
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Upon compressing perceptually relevant signals, conventional quantization generally results in unnaturaloutcomes at low rates. We propose distribution preserving quantization (DPQ) to solve this problem.DPQ is a new quantization concept that confines the probability space of the reconstruction to be identicalto that of the source. A distinctive feature of DPQ is that it facilitates a seamless transition between signalsynthesis and quantization. A theoretical analysis of DPQ leads to a distribution preserving rate-distortionfunction (DP-RDF), which serves as a lower bound on the rate of any DPQ scheme, under a constrainton distortion. In general situations, the DP-RDF approaches the classic rate-distortion function for thesame source and distortion measure, in the limit of an increasing rate. A practical DPQ scheme basedon a multivariate transformation is also proposed. This scheme asymptotically achieves the DP-RDF fori.i.d. Gaussian sources and the mean squared error.

Keyword
Distribution preserving quantization, Rate-distortion function, Shannon lower bound
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-38515 (URN)
Note
QC 20110829Available from: 2011-08-29 Created: 2011-08-26 Last updated: 2011-08-29Bibliographically approved
4. Asymptotically Optimal Distribution Preserving Quantization for Stationary Gaussian Processes
Open this publication in new window or tab >>Asymptotically Optimal Distribution Preserving Quantization for Stationary Gaussian Processes
(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
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:nbn:se:kth:diva-38517 (URN)
Note
QC 20110829Available from: 2011-08-29 Created: 2011-08-26 Last updated: 2011-08-29Bibliographically approved
5. Multiple Description Distribution Preserving Quantization
Open this publication in new window or tab >>Multiple Description Distribution Preserving Quantization
2013 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 24, 6410-6422 p.Article in journal (Refereed) Published
Abstract [en]

The notion of a multiple description quantizer (MDQ) includes providing multiple distortion levels. If a human observer is involved, the design of MDQ requires a suitable distortion measure to achieve a graceful quality degradation in the case of description losses. While the mean squared error is a ubiquitous distortion measure for many classic MDQ schemes, it is known to be perceptually relevant only at low distortions. We propose a new MDQ designed according to an unconventional distortion criterion that combines the mean squared error with a constraint on the probability distribution of the reconstructed signal. The performance of the new MDQ is shown to approach that of the classic MDQ asymptotically as rate increases. However, once applied in the context of transform audio coding, the new MDQ significantly outperforms a classic MDQ in perceptual tests. The new scheme is suitable for a wide range of distortions and renders a seamless transition between coding that preserves signal features and coding of a waveform.

Keyword
Distribution preserving quantization (DPQ), multiple description coding (MDC)
National Category
Computer and Information Science Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-38518 (URN)10.1109/TSP.2013.2286773 (DOI)000327259500022 ()2-s2.0-84888609887 (Scopus ID)
Note

QC 20131219

Available from: 2011-08-26 Created: 2011-08-26 Last updated: 2017-12-08Bibliographically approved
6. Sequential Entropy Coding of Quantization Indices with Update Recursion on Probability
Open this publication in new window or tab >>Sequential Entropy Coding of Quantization Indices with Update Recursion on Probability
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In lossy coding, quantization indices generally contain dependencies. Encoding of quantization indices requires an entropy coding method that exploits these dependencies efficiently. In this article, we propose an entropy coding method that encodes quantization indices sequentially using a recursive update on the probability distribution of each index conditioned on all past indices and available side information. The method is based on a generic model of a lossy coding system and hence can be applied to a large range of lossy coding scenarios. An application of the proposed method to lossy coding of signals that can be described within a linear stochastic system is studied. The method is evaluated in two rate-distortion optimized lossy coding systems, and its efficiency is confirmed by the results.

National Category
Computer and Information Science
Identifiers
urn:nbn:se:kth:diva-38549 (URN)
Note
QC 20110829Available from: 2011-08-29 Created: 2011-08-29 Last updated: 2011-08-29Bibliographically approved

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