High-rate quantization and transform coding with side information at the decoder

Rebollo-Monedero, David; Rane, Shantanu; Aaron, Anne; Girod, Bernd

doi:10.1016/j.sigpro.2006.03.015

Cited by 32 publications

(34 citation statements)

References 60 publications

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“…Thus, is minimized by (8) The resulting minimal distortion is (9) where we have introduced a notation for the quasi-norm. For the variable-rate optimization, we use Jensen's inequality rather than Hölder's inequality:…”

Section: Lemmamentioning

confidence: 99%

Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions

Misra

Goyal

Varshney

2011

IEEE Trans. Inform. Theory

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Abstract-Communication of quantized information is frequently followed by a computation. We consider situations of distributed functional scalar quantization: distributed scalar quantization of (possibly correlated) sources followed by centralized computation of a function. Under smoothness conditions on the sources and function, companding scalar quantizer designs are developed to minimize mean-squared error (MSE) of the computed function as the quantizer resolution is allowed to grow. Striking improvements over quantizers designed without consideration of the function are possible and are larger in the entropy-constrained setting than in the fixed-rate setting. As extensions to the basic analysis, we characterize a large class of functions for which regular quantization suffices, consider certain functions for which asymptotic optimality is achieved without arbitrarily fine quantization, and allow limited collaboration between source encoders. In the entropy-constrained setting, a single bit per sample communicated between encoders can have an arbitrarily large effect on functional distortion. In contrast, such communication has very little effect in the fixed-rate setting.Index Terms-Asymptotic quantization theory, distributed source coding, optimal point density function, rate-distortion theory.

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Section: Lemmamentioning

confidence: 99%

Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions

Misra

Goyal

Varshney

2011

IEEE Trans. Inform. Theory

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“…Specifically, since , we find that . This implies that (as in (15)) simplifies to (34) and the local KLT takes the following simple shape. …”

Section: B the Conditional Klt Andmentioning

confidence: 99%

The Distributed Karhunen–Loève Transform

Gastpar

Dragotti

Vetterli

2006

IEEE Trans. Inform. Theory

180

222

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Abstract-The Karhunen-Loève transform (KLT) is a key element of many signal processing and communication tasks. Many recent applications involve distributed signal processing, where it is not generally possible to apply the KLT to the entire signal; rather, the KLT must be approximated in a distributed fashion. This paper investigates such distributed approaches to the KLT, where several distributed terminals observe disjoint subsets of a random vector.We introduce several versions of the distributed KLT. First, a local KLT is introduced, which is the optimal solution for a given terminal, assuming all else is fixed. This local KLT is different and in general improves upon the marginal KLT which simply ignores other terminals. Both optimal approximation and compression using this local KLT are derived. Two important special cases are studied in detail, namely, the partial observation KLT which has access to a subset of variables, but aims at reconstructing them all, and the conditional KLT which has access to side information at the decoder. We focus on the jointly Gaussian case, with known correlation structure, and on approximation and compression problems. Then, the distributed KLT is addressed by considering local KLTs in turn at the various terminals, leading to an iterative algorithm which is locally convergent, sometimes reaching a global optimum, depending on the overall correlation structure. For compression, it is shown that the classical distributed source coding techniques admit a natural transform coding interpretation, the transform being the distributed KLT. Examples throughout illustrate the performance of the proposed distributed KLT. This distributed transform has potential applications in sensor networks, distributed image databases, hyper-spectral imagery, and data fusion.

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“…For example, when the source is Gaussian, it has been shown that the KLT is still the best transform and it is optimal in some cases [20]. Other optimality conditions for transforms in high bit-rate regimes have also been proved [18,42]. If, however, the Gaussian and high bit rate assumptions are relaxed then the problem of distributed transform coding remains largely open.…”

Section: Original Contributionmentioning

confidence: 99%

Centralized and Distributed Semiparametric Compression of Piecewise Smooth Functions

Chaisinthop

Dragotti

2011

IEEE Trans. Signal Process.

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This thesis introduces novel wavelet-based semi-parametric centralized and distributed compression methods for a class of piecewise smooth functions. Our proposed compression schemes are based on a non-conventional transform coding structure with simple independent encoders and a complex joint decoder.Current centralized state-of-the-art compression schemes are based on the conventional structure where an encoder is relatively complex and nonlinear. In addition, the setting usually allows the encoder to observe the entire source. Recently, there has been an increasing need for compression schemes where the encoder is lower in complexity and, instead, the decoder has to handle more computationally intensive tasks. Furthermore, the setup may involve multiple encoders, where each one can only partially observe the source. Such scenario is often referred to as distributed source coding.In the first part, we focus on the dual situation of the centralized compression where the encoder is linear and the decoder is nonlinear. Our analysis is centered around a class of 1-D piecewise smooth functions. We show that, by incorporating parametric estimation into the decoding procedure, it is possible to achieve the same distortionrate performance as that of a conventional wavelet-based compression scheme. We also present a new constructive approach to parametric estimation based on the sampling results of signals with finite rate of innovation.The second part of the thesis focuses on the distributed compression scenario, where each independent encoder partially observes the 1-D piecewise smooth function. We propose a new wavelet-based distributed compression scheme that uses parametric estiiii mation to perform joint decoding. Our distortion-rate analysis shows that it is possible for the proposed scheme to achieve that same compression performance as that of a joint encoding scheme.Lastly, we apply the proposed theoretical framework in the context of distributed image and video compression. We start by considering a simplified model of the video signal and show that we can achieve distortion-rate performance close to that of a joint encoding scheme. We then present practical compression schemes for real world signals.Our simulations confirm the improvement in performance over classical schemes, both in terms of the PSNR and the visual quality.iv

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High-rate quantization and transform coding with side information at the decoder

Cited by 32 publications

References 60 publications

Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions

Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions

The Distributed Karhunen–Loève Transform

Centralized and Distributed Semiparametric Compression of Piecewise Smooth Functions

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