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Ashish Jagmohan - One of the best experts on this subject based on the ideXlab platform.
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on the operational rate distortion performance of uniform Scalar Quantization based wyner ziv coding of laplace markov sources
IEEE Transactions on Multimedia, 2008Co-Authors: V Sheinin, Ashish JagmohanAbstract:Wyner-Ziv (WZ) coding has recently been proposed as a low encoding complexity alternative to traditional DPCM coding for compression of sources with memory, in particular, in applications like multimedia compression. The viability of this alternative approach clearly depends on the compression performance of WZ coding compared to that of DPCM coding. In an attempt to understand the performance gap between WZ coding and DPCM coding, this paper studies the operational rate-distortion performance of WZ coding, using uniform Scalar Quantization followed by perfect Slepian-Wolf coding, for compression of a Laplace-Markov (LM) source. It is shown that at low rates or for weakly correlated LM sources, WZ coding is indeed a competitive alternative to DPCM coding. However, at high rates the performance gap becomes non-negligible for strongly correlated LM sources. In order to reduce the gap at high rates, a hybrid approach that combines DPCM coding and WZ coding is further investigated. It is shown that the hybrid approach is indeed competitive to DPCM coding at all rates even for strongly correlated LM sources.
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low rate hybrid wyner ziv coding of laplace markov source using uniform Scalar Quantization
International Conference on Acoustics Speech and Signal Processing, 2008Co-Authors: V Sheinin, Ashish JagmohanAbstract:Hybrid Wyner-Ziv coders which employ a combination of Wyner-Ziv coding and differential pulse code modulation (DPCM) encoding have recently gained popularity for applications such as video coding. In this paper we analyze the low-rate operational rate distortion performance of Wyner-Ziv coding using uniform Scalar Quantization, in the context of such hybrid coders. Motivated by video we consider the compression of a first-order Laplace-Markov source, and derive approximate analytical rate and distortion expressions which are accurate at low rates. We utilize the derived analytical expressions to address the problem of determining the optimal Quantization interval ratio of the Wyner-Ziv and DPCM Scalar quantizers, for a range of rates.
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uniform Scalar Quantization based wyner ziv coding of laplace markov source
International Conference on Acoustics Speech and Signal Processing, 2007Co-Authors: V Sheinin, Ashish JagmohanAbstract:Wyner-Ziv coding has recently emerged as an alternative to conventional DPCM coding for compression of sources with memory, particularly in video compression. This paper studies the operational rate-distortion performance of Wyner-Ziv coding, using uniform Scalar Quantization followed by perfect Slepian-Wolf coding, for compression of a Laplace-Markov source. The performance gap of this technique relative to DPCM coding is characterized through derived rate-distortion expressions and numerical simulations.
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low rate uniform Scalar Quantization of memoryless gaussian sources
International Conference on Image Processing, 2006Co-Authors: V Sheinin, Ashish JagmohanAbstract:The low-rate (< 1 bits per sample) operational rate-distortion performance of uniform Scalar quantizers for the memoryless Gaussian source is studied. Approximate analytical expressions for the operational rate-distortion function are derived, and the accuracy of the derived function is verified through simulation. It is shown that in the zero-rate limit the derived operational rate-distortion function is first-order optimal with respect to the Shannon lower bound. The derived function is used to study the performance of uniform Scalar quantizers for the Gaussian Wyner-Ziv problem. Lastly, the derived low-rate rate-distortion function is used to provide improved low-rate bit allocation for jointly Gaussian vectors.
David L Neuhoff - One of the best experts on this subject based on the ideXlab platform.
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on the convexity of the mse distortion of symmetric uniform Scalar Quantization
IEEE Transactions on Information Theory, 2018Co-Authors: David L NeuhoffAbstract:This paper investigates the convexity of the mean squared-error distortion of symmetric uniform Scalar Quantization with respect to step size. The principal results include proofs for odd numbers of levels that distortion is not convex for any symmetric density and that it is convex for even numbers of levels for densities, such as Gaussian, Laplacian, and gamma, but is not, in general for two-sided Rayleigh. For the latter case, an interval is derived that includes the optimal step size and over which the distortion is convex. The proofs of convexity use the Euler–Maclaurin formula applied to the second derivative of distortion, with upper bounds on the remainder term. These results imply that a zero of the derivative of the distortion for these densities, which has been previously conjectured optimal, is indeed the optimal step size, because the distortion is convex either globally or locally over a sufficiently wide interval to ensure a global minimizer.
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information rates of densely sampled data distributed vector Quantization and Scalar Quantization with transforms for gaussian sources
IEEE Transactions on Information Theory, 2013Co-Authors: David L Neuhoff, Sandeep S PradhanAbstract:This paper establishes rates attainable by several lossy schemes for coding a continuous parameter source to a specified mean-squared-error distortion based on sampling at asymptotically large rates. First, a densely sampled, spatiotemporal, stationary Gaussian source is distributively encoded. The Berger-Tung bound to the distributed rate-distortion function and three convergence theorems are used to obtain an upper bound, expressed in terms of the source spectral density, to the smallest attainable rate at asymptotically large sampling rates. The bound is tighter than that recently obtained by Kashyap Both indicate that with ideal distributed lossy coding, dense sensor networks can efficiently sense and convey a field, in contrast to the negative result obtained by Marco for encoders based on Scalar Quantization and Slepian-Wolf distributed lossless coding. The second scheme is transform coding with Scalar coefficient Quantization. A new generalized transform coding analysis, as well as the aforementioned convergence theorems, is used to find the smallest attainable rate at asymptotically large sampling rates in terms of the source spectral density and the operational rate-distortion function of the family of quantizers, which in contrast to previous analyses need not be convex. The result shows that when a transform is used, Scalar Quantization need not cause the poor performance found by Marco As a corollary, the final result pursues an approach, originally proposed by Berger, to show that the inverse water-pouring formula for the rate-distortion function can be attained at high sampling rates by transform coding with ideal vector Quantization to encode the coefficients. Also established in the paper are relations between operational rate-distortion and distortion-rate functions for a continuous parameter source and those for the discrete parameter source that results from sampling.
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asymptotic mse distortion of mismatched uniform Scalar Quantization
IEEE Transactions on Information Theory, 2012Co-Authors: David L NeuhoffAbstract:Asymptotic formulas are derived for the mean-squared error (MSE) distortion of N-level uniform Scalar quantizers designed to be MSE optimal for one density function, but applied to another, as N → ∞. These formulas, which are based on the Euler-Maclaurin formula, are then applied with generalized gamma, Bucklew-Gallagher, and Hui-Neuhoff density functions as the designed-for and applied-to densities. It is found that the mismatch between the designed-for and applied-to densities can disturb the delicate balance between granular and overload distortions in optimal Quantization, with the result that, generally speaking, the granular or overload distortion dominates, respectively, depending on whether the applied-to density function has a lighter or heavier tail than the designed-for density. Specifically, in the case of generalized gamma densities, a variance mismatch makes overload distortion dominate for an applied-to source with a slightly larger variance, whereas a shape mismatch can tolerate a wider variance difference while retaining the dominance of the granular distortion. In addition, for the studied density functions, the Euler-Maclaurin approach is used to derive asymptotic formulas for the optimal quantizer step size in a simpler, more direct, way than previous approaches.
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Low-resolution Scalar Quantization for Gaussian sources and squared error
IEEE Transactions on Information Theory, 2006Co-Authors: D. Marco, David L NeuhoffAbstract:This correspondence analyzes the low-resolution performance of entropy-constrained Scalar Quantization. It focuses mostly on Gaussian sources, for which it is shown that for both binary quantizers and infinite-level uniform threshold quantizers, as D approaches the source variance /spl sigma//sup 2/, the least entropy of such quantizers with mean-squared error D or less approaches zero with slope -log/sub 2/e/2/spl sigma//sup 2/. As the Shannon rate-distortion function approaches zero with the same slope, this shows that in the low-resolution region, Scalar Quantization with entropy coding is asymptotically as good as any coding technique.
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performance of low rate entropy constrained Scalar quantizers
Unknown Journal, 2004Co-Authors: D. Marco, David L NeuhoffAbstract:The operational rate-distortion function of entropy-constrained Scalar quantizers in the asymptotic low resolution regime, for memoryless Gaussian sources, is investigated. It is shown that asymptotically, as distortion tends to variance, or equivalently as rate tends to zero, the operational rate-distortion function matches the Shannon rate-distortion function. This implies that Scalar Quantization is asymptotically optimal, a fact not previously known.
V Sheinin - One of the best experts on this subject based on the ideXlab platform.
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on the operational rate distortion performance of uniform Scalar Quantization based wyner ziv coding of laplace markov sources
IEEE Transactions on Multimedia, 2008Co-Authors: V Sheinin, Ashish JagmohanAbstract:Wyner-Ziv (WZ) coding has recently been proposed as a low encoding complexity alternative to traditional DPCM coding for compression of sources with memory, in particular, in applications like multimedia compression. The viability of this alternative approach clearly depends on the compression performance of WZ coding compared to that of DPCM coding. In an attempt to understand the performance gap between WZ coding and DPCM coding, this paper studies the operational rate-distortion performance of WZ coding, using uniform Scalar Quantization followed by perfect Slepian-Wolf coding, for compression of a Laplace-Markov (LM) source. It is shown that at low rates or for weakly correlated LM sources, WZ coding is indeed a competitive alternative to DPCM coding. However, at high rates the performance gap becomes non-negligible for strongly correlated LM sources. In order to reduce the gap at high rates, a hybrid approach that combines DPCM coding and WZ coding is further investigated. It is shown that the hybrid approach is indeed competitive to DPCM coding at all rates even for strongly correlated LM sources.
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low rate hybrid wyner ziv coding of laplace markov source using uniform Scalar Quantization
International Conference on Acoustics Speech and Signal Processing, 2008Co-Authors: V Sheinin, Ashish JagmohanAbstract:Hybrid Wyner-Ziv coders which employ a combination of Wyner-Ziv coding and differential pulse code modulation (DPCM) encoding have recently gained popularity for applications such as video coding. In this paper we analyze the low-rate operational rate distortion performance of Wyner-Ziv coding using uniform Scalar Quantization, in the context of such hybrid coders. Motivated by video we consider the compression of a first-order Laplace-Markov source, and derive approximate analytical rate and distortion expressions which are accurate at low rates. We utilize the derived analytical expressions to address the problem of determining the optimal Quantization interval ratio of the Wyner-Ziv and DPCM Scalar quantizers, for a range of rates.
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uniform Scalar Quantization based wyner ziv coding of laplace markov source
International Conference on Acoustics Speech and Signal Processing, 2007Co-Authors: V Sheinin, Ashish JagmohanAbstract:Wyner-Ziv coding has recently emerged as an alternative to conventional DPCM coding for compression of sources with memory, particularly in video compression. This paper studies the operational rate-distortion performance of Wyner-Ziv coding, using uniform Scalar Quantization followed by perfect Slepian-Wolf coding, for compression of a Laplace-Markov source. The performance gap of this technique relative to DPCM coding is characterized through derived rate-distortion expressions and numerical simulations.
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low rate uniform Scalar Quantization of memoryless gaussian sources
International Conference on Image Processing, 2006Co-Authors: V Sheinin, Ashish JagmohanAbstract:The low-rate (< 1 bits per sample) operational rate-distortion performance of uniform Scalar quantizers for the memoryless Gaussian source is studied. Approximate analytical expressions for the operational rate-distortion function are derived, and the accuracy of the derived function is verified through simulation. It is shown that in the zero-rate limit the derived operational rate-distortion function is first-order optimal with respect to the Shannon lower bound. The derived function is used to study the performance of uniform Scalar quantizers for the Gaussian Wyner-Ziv problem. Lastly, the derived low-rate rate-distortion function is used to provide improved low-rate bit allocation for jointly Gaussian vectors.
Pascal Frossard - One of the best experts on this subject based on the ideXlab platform.
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balanced multiple description Scalar Quantization
International Symposium on Information Theory, 2008Co-Authors: I Radulovic, Pascal FrossardAbstract:This paper tackles the problem of the generation of an arbitrary number of balanced descriptions with multiple description Scalar Quantization (MDSQ). We show how, with a very low complexity, we can vary the number of descriptions and the redundancy between them, in order to adapt to different channel characteristics. A comparison with state-of-the-art MDSQ schemes shows a better performance of our solution in terms of an average distortion at the receiver, which comes from the flexibility of our solution to better adapt to various lossy conditions.
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fast index assignment for balanced n description Scalar Quantization
Data Compression Conference, 2005Co-Authors: I Radulovic, Pascal FrossardAbstract:Summary form only given. We address the design of any number of balanced descriptions with multiple description Scalar quantizers (MDSQ), using fast index assignment methods. Such systems proceed in two steps, Scalar Quantization and index assignment, that map the quantized value to an N-tuple of Quantization indices, to be sent over N channels. We address the specific balanced scenario, where all descriptions have equal rates and where any subset of k out of N descriptions induces the same distortion. We propose two simple index assignment schemes for uniform sources, that are able to generate any number, N (greater than 2), of such balanced descriptions, at any coding rate. The case of Gaussian distributions is also addressed using companding.
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index assignment for n balanced multiple description Scalar Quantization
2005Co-Authors: I Radulovic, Pascal FrossardAbstract:In this paper, we address the design of any number of balanced multiple descriptions using the multiple description Scalar Quantization(MDSQ) technique. The proposed scheme has the advantages of low complexity, the possibility of being extended easily to any number of descriptions and the possibility to trade off between the side, partial and central distortions. Unlike existing schemes, it can produce balanced descriptions at low rates, at the price however of a slightly higher distortion. The behavior of the proposed index assignment at high rate is in the same time similar to state-of-the-art schemes. The proposed scheme offers the possibility to adapt to loss probability, and rate constraints, in playing with both the number of descriptions, and the rate of each of them, to minimize the average distortion. The comparison with the systematic FEC (N; k) scheme shows that the FEC scheme in general gives smaller average distortion, but that our scheme seems to be more robust to sudden changes in network conditions and that receiving all the descriptions in general gives smaller distortions.
Sheila S. Hemami - One of the best experts on this subject based on the ideXlab platform.
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Universal multiple description Scalar Quantization: analysis and design
IEEE Transactions on Information Theory, 2004Co-Authors: Chao Tian, Sheila S. HemamiAbstract:This paper introduces a new high-rate analysis of the multiple description Scalar quantizer (MDSQ) with balanced descriptions. The analysis provides insight into the structure of the MDSQ, suggesting the nonoptimality of uniform central quantizer cell lengths, as well as a method to approximate optimal cell lengths. For both level-constrained and entropy-constrained MDSQ, new upper bounds on the granular distortion for sources with smooth probability density functions (pdfs) are derived under the mean-squared error measure, which are 0.4 dB lower than previous results. Based on the insights, a universal multiple description Scalar quantizer (UMDSQ) is proposed which, at high rate, can achieve nearly the same performance as the fully optimized entropy-constrained MDSQ (ECMDSQ), without requiring extensive training. The proposed UMDSQ has only two control parameters, and a continuum of tradeoff points between the central and side distortions can be achieved as the two parameters are varied.
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universal multiple description Scalar Quantization analysis and design
Data Compression Conference, 2003Co-Authors: Chao Tian, Sheila S. HemamiAbstract:A new high-rate analysis of the entropy-constrained multiple description Scalar quantizer (ECMDSQ) is introduced. The analysis provides insight into the structure of the ECMDSQ, suggesting the non-optimality of uniform central quantizer cells with finite diagonals in the index assignment matrix, as well as a method to approximate optimal cell sizes. Based on these insights, a universal multiple description Scalar quantizer (UMDSQ) is proposed which can achieve nearly the same performance as the fully optimized ECMDSQ, at much lower design complexity. The design requires selection of only two parameters, and the resulting UMDSQ can provide a continuum of trade-off points between the central and side distortions as the two parameters are varied.
