Scalar Quantizers

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 5181 Experts worldwide ranked by ideXlab platform

David L Neuhoff - One of the best experts on this subject based on the ideXlab platform.

  • Monotonicity of Step Sizes of MSE-Optimal Symmetric Uniform Scalar Quantizers
    IEEE Transactions on Information Theory, 2019
    Co-Authors: David L Neuhoff
    Abstract:

    For generalized gamma probability densities, this paper studies the monotonicity of step sizes of optimal symmetric uniform Scalar Quantizers with respect to mean squared-error distortion. The principal results are that for the special cases of Gaussian, Laplacian, two-sided Rayleigh, and gamma densities, optimal step size monotonically decreases when the number of levels $N$ increases by two, and that for any generalized gamma density and all sufficiently large $N$ , optimal step size again decreases when $N$ increases by two. Also, it is shown that for a Laplacian density and sufficiently large $N$ , optimal step size decreases when $N$ increases by just one.

  • the validity of the additive noise model for uniform Scalar Quantizers
    IEEE Transactions on Information Theory, 2005
    Co-Authors: D. Marco, David L Neuhoff
    Abstract:

    A uniform Scalar quantizer with small step size, large support, and midpoint reconstruction levels is frequently modeled as adding orthogonal noise to the quantizer input. This paper rigorously demonstrates the asymptotic validity of this model when the input probability density function (pdf) is continuous and satisfies several other mild conditions. Specifically, as step size decreases, the correlation between input and quantization error becomes negligible relative to the mean-squared error (MSE). The model is even valid when the input density is discontinuous at the origin, but discontinuities elsewhere can prevent the correlation from being negligible. Though this invalidates the additive model, an asymptotic formula for the correlation is found in terms of the step size and the heights and positions of the discontinuities. For a finite support input density, such as uniform, it is shown that the support of the uniform quantizer can be matched to that of the density in ways that make the correlation approach a variety of limits. The derivations in this paper are based on an analysis of the asymptotic convergence of cell centroids to cell midpoints. This convergence is fast enough that the centroids and midpoints induce the same asymptotic MSE, but not fast enough to induce the same correlations.

  • ISIT - A fast, flexible and robust design method for noisy channel Scalar quantization
    Proceedings. International Symposium on Information Theory 2005. ISIT 2005., 2005
    Co-Authors: P.j. Pelzl, David L Neuhoff
    Abstract:

    This paper presents a new method for designing noisy channel Scalar Quantizers, which is fast, more robust to initial conditions, and more amenable to a variety of distortion criteria

  • performance of low rate entropy constrained Scalar Quantizers
    Unknown Journal, 2004
    Co-Authors: D. Marco, David L Neuhoff
    Abstract:

    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.

  • on the support of mse optimal fixed rate Scalar Quantizers
    IEEE Transactions on Information Theory, 2001
    Co-Authors: David L Neuhoff
    Abstract:

    This paper determines how the support regions of optimal and asymptotically optimal fixed-rate Scalar Quantizers (with respect to mean-squared error) depend on the number of quantization points N and the probability density of the variable being quantized. It shows that for asymptotic optimality it is necessary and sufficient that the support region grow fast enough that the outer (or overload) distortion decreases as o(1/N/sup 2/). Formulas are derived for the minimal support of asymptotically optimal Quantizers for generalized gamma densities, including Gaussian and Laplacian. Interestingly, these turn out to be essentially the same as for the support of optimal fixed-rate uniform Scalar Quantizers. Heuristic arguments are then used to find closed-form estimates for the support of truly optimal Quantizers for generalized gamma densities. These are found to be more accurate than the best prior estimates, as computed by numerical algorithms. They demonstrate that the support of an optimal quantizer is larger than the minimal asymptotically optimal support by a factor depending on the density but not N, and that the outer distortion of optimal Quantizers decreases as 1/N/sup 3/.

N Farvardin - One of the best experts on this subject based on the ideXlab platform.

  • fixed rate successively refinable Scalar Quantizers
    Data Compression Conference, 1996
    Co-Authors: H Brunk, N Farvardin
    Abstract:

    The problem of successively refinable scaler quantizer design is considered. The weighted average of the expected distortion at each level of refinement is used as a quantizer figure of merit. Quantizers designed using this criterion can find application in many practical situations. Algorithms are presented for the design of both uniform and non-uniform Quantizers and performance of Quantizers designed for several sources using these algorithms is presented and compared with the performance of other Scalar Quantizers.

  • Switched Scalar Quantizers for hidden Markov sources
    IEEE Transactions on Information Theory, 1992
    Co-Authors: D.m. Goblirsch, N Farvardin
    Abstract:

    An algorithm for designing switched Scalar Quantizers for hidden Markov sources is described. The design problem is cast as a nonlinear optimization problem. The optimization variables are the thresholds and reproduction levels for each quantizer and the parameters defining the next-quantizer map. The cost function is the average distribution incurred by the system in steady-state. The next-quantizer map is treated as a stochastic map so that all of the optimization variables are continuous-valued, allowing the use of a gradient-based optimization procedure. This approach solves a major problem in the design of switched Scalar quantizing systems, namely, that of determining an optimal next-quantizer decision rule. Details are given for computing the cost function and its gradient for weighted-squared-error distortion. Simulation results which compare the new system to current systems show that the present system performs better. It is observed that the optimal system can in fact have a next-quantizer map with stochastic components. >

  • Data Compression Conference - Fixed-rate successively refinable Scalar Quantizers
    Proceedings of Data Compression Conference - DCC '96, 1
    Co-Authors: H Brunk, N Farvardin
    Abstract:

    The problem of successively refinable scaler quantizer design is considered. The weighted average of the expected distortion at each level of refinement is used as a quantizer figure of merit. Quantizers designed using this criterion can find application in many practical situations. Algorithms are presented for the design of both uniform and non-uniform Quantizers and performance of Quantizers designed for several sources using these algorithms is presented and compared with the performance of other Scalar Quantizers.

  • Data Compression Conference - Entropy-constrained successively refinable Scalar quantization
    Proceedings DCC '97. Data Compression Conference, 1
    Co-Authors: Hamid Jafarkhani, H Brunk, N Farvardin
    Abstract:

    We study the design of entropy-constrained successively refinable Scalar Quantizers. We propose two algorithms to minimize the average distortion and design such a quantizer. We consider two sets of constraints on the entropy: (i) constraint on the average rate and (ii) constraint on aggregate rates. Both algorithms can be easily extended to design vector Quantizers.

Sorina Dumitrescu - One of the best experts on this subject based on the ideXlab platform.

  • bit error resilient index assignment for multiple description Scalar Quantizers
    IEEE Transactions on Information Theory, 2015
    Co-Authors: Sorina Dumitrescu
    Abstract:

    This paper addresses the problem of increasing the robustness to bit errors for two description Scalar Quantizers. Our approach is to start with an $m$ -diagonal index assignment and further apply a permutation to the indexes of each description to increase the minimum Hamming distance $d_{\rm min}$ of the set of valid index pairs. In particular, we show how to construct linear permutation pairs achieving $d_{\rm min}\geq 3$ , and establish a lower bound in terms of the description rate $R$ , for the highest value of $m$ for which such permutations exist.

  • bit error resilient index assignment for multiple description Scalar Quantizers
    International Symposium on Information Theory, 2013
    Co-Authors: Sorina Dumitrescu
    Abstract:

    This work addresses the problem of increasing the robustness to bit errors for two description Scalar Quantizers. To this aim a permutation is applied to the indices of each description. We show how to construct permutation pairs that increase the minimum Hamming distance of the set of valid index pairs to 3 when the redundancy is sufficiently high. Additionally, for the case when one description is known to be correct we propose a new performance criterion, denoted by dside,min. This represents the minimum Hamming distance of the set of valid indices of one description, when the index of the other description is fixed. We develop a technique for constructing permutation pairs achieving dside,min ≥ h based on a linear (R, [log2 m]) channel code of minimum Hamming distance h + 1, where R is the rate of each description and m is the number of diagonals occupied by the valid index pairs in the matrix of the initial index assignment.

  • index assignment capable of detecting one bit errors for multiple description Scalar Quantizers
    Cyberworlds, 2013
    Co-Authors: Yinghan Wan, Sorina Dumitrescu
    Abstract:

    This work is concerned with increasing the error resilience of two description Scalar Quantizers by applying a permutation to the index of each description, for an m-diagonal initial index assignment. First we address the existence of permutations achieving a minimum Hamming distance of at least 2. Such permutations allow the central decoder to detect any 1 bit error pattern. We establish the connection with the hypercube antibandwidth problem, connection which allows us to determine the highest value of m for which such a permutation exists and to show its construction. Further, we highlight the relation between the error robustness at the side decoders and the bandwidth of the hypercube labeling associated to the permutation. To ensure error resilience at both the central and side decoders we are interested in labelings with the lowest bandwidth given that the antibandwidth is larger or equal to m. We make some progress toward the solution of this problem by constructing a class of hypercube labelings trading the increase in antibandwidth for the decrease in bandwidth.

  • on properties of locally optimal multiple description Scalar Quantizers with convex cells
    IEEE Transactions on Information Theory, 2009
    Co-Authors: Sorina Dumitrescu
    Abstract:

    It is known that the generalized Lloyd method is applicable to locally optimal multiple description Scalar quantizer (MDSQ) design. However, it remains unsettled when the resulting MDSQ is also globally optimal. We partially answer the above question by proving that for a fixed index assignment there is a unique locally optimal fixed-rate MDSQ of convex cells under Trushkin's sufficient conditions for the uniqueness of locally optimal fixed-rate single description Scalar quantizer. This result holds for fixed-rate multiresolution Scalar quantizer (MRSQ) of convex cells as well. Thus, the well-known log-concave probability density function (pdf) condition can be extended to the multiple description and multiresolution cases.

  • speed up of encoder optimization step in multiple description Scalar quantizer design
    Data Compression Conference, 2008
    Co-Authors: Sorina Dumitrescu
    Abstract:

    The design of optimal multiple description Scalar Quantizers was pioneered by Vaishampayan with a generalization of Lloyd's algorithm, which alternatively optimizes the decoder, respectively the encoder, while the other component is fixed. We propose an algorithm which speeds up the encoder optimization step from O(N 2) to O(N log N) time complexity, where N is the number of cells in the central partition.

Peter Schelkens - One of the best experts on this subject based on the ideXlab platform.

  • Authors ’ affiliations:
    2014
    Co-Authors: A.i. Gavrilescu, Adrian Munteanu, Peter Schelkens, J Cornelis
    Abstract:

    Equation Section 1Abstract: A new class of Embedded Multiple Description Scalar Quantizers (EMDSQ) is proposed. EMDSQ meet the desired features of high redundancy level, fine grain rate adaptation and progressive transmission of each description. Experimental results show that EMDSQ yield better rate-distortion performance in comparison to Multiple Description Uniform Scalar Quantizers (MDUSQ) previously proposed in the literature. Introduction: Multiple Description Coding (MDC) was introduced to efficiently overcome the channel impairments over diversity-based systems by allowing decoders to extract meaningful information from a subset of the bit-stream. Previous research focused on finding the optimal achievable rate-distortion regions [1], followed by the design of practical compression systems [2] to meet these theoretical boundaries. For robust communicatio

  • an optimization algorithm for scalable multiple description Scalar Quantizers
    International Symposium on Information Theory and its Applications, 2012
    Co-Authors: Shahid M Satti, Adrian Munteanu, Peter Schelkens, Nikos Deligiannis, J Cornelis
    Abstract:

    A scalable multiple description Scalar quantizer (SMDSQ) is a quantization based framework used for scalable multiple description coding (SMDC). In this paper, we introduce a novel generalization of the Lloyd-Max algorithm to realize locally optimal SMDSQs. Both level-constrained and entropy-constrained cases are considered. For both cases, locally optimal solutions are realized by iterative execution of the centroid and the modified nearest-neighbor conditions. Experimental results confirm that, for a zero-mean unit-variance Gaussian source, the optimization algorithm enables a significant reduction in distortion for the level-constrained case. Moreover, relatively lesser but still significant distortion-rate (D-R) gains are viable for the entropy-constrained case. It is shown that, for a packetized transmission of Gaussian as well as wavelet-decomposed images, the obtained optimization gains translate into an average improvement in the decoder's signal-to-noise-ratio (SNR) for a wide range of packet loss rates.

  • a new family of embedded multiple description Scalar Quantizers image coding applications
    International Conference on Image Processing, 2004
    Co-Authors: A.i. Gavrilescu, Adrian Munteanu, J Cornelis, Peter Schelkens
    Abstract:

    A new family of embedded multiple description Scalar Quantizers (EMDSQ) that support the progressive transmission of images over variable-bandwidth error-prone channels is proposed in this paper. A control mechanism that allows for tuning the redundancy between the two descriptions for each quantization level is also designed. The employed mechanism enables control of the tradeoff between the coding efficiency and error-resilience, and provides an increased robustness by improving the error resilience in the most important layers of the embedded bit-streams. Instantiations of the proposed family are incorporated in a wavelet-based embedded coding system, and the redundancy-control mechanism is practically demonstrated. Experimental results show that the proposed EMDSQ outperform the state-of-the-art multiple description uniform Scalar Quantizers (MDUSQ) previously proposed in the literature for error-resilient progressive image transmission.

  • embedded multiple description Scalar Quantizers and wavelet based quadtree coding for progressive image transmission over unreliable channels
    European Signal Processing Conference, 2004
    Co-Authors: A.i. Gavrilescu, Adrian Munteanu, J Cornelis, Peter Schelkens
    Abstract:

    In this paper, we present a new Multiple Description Coding (MDC) system that enables the progressive transmission of images over unreliable channels with variable bandwidth. The proposed system employs a new type of Quantizers, called Embedded Multiple Description Scalar Quantizers (EMDSQ). The system relies on wavelet-based QuadTree (QT) coding of the significance maps to encode the Quantizers' output, and is referred to as Multiple Description-QT (MD-QT) coding. The EMDSQ enables the MD-QT coder to provide bit-streams that meet the desired features consisting of a high redundancy level, fine-grain rate adaptation and progressive transmission of each description. Experimental results show that the proposed MD-QT system based on EMDSQ yields better rate-distortion performance in comparison to MD-QT employing the embedded Multiple Description Uniform Scalar Quantizers (MDUSQ) previously proposed in the literature.

  • On the optimality of embedded deadzone Scalar-Quantizers for wavelet-based L-infinite-constrained image coding
    IEEE Signal Processing Letters, 2004
    Co-Authors: A. Alecu, Adrian Munteanu, J Cornelis, Steven Dewitte, Peter Schelkens
    Abstract:

    In wavelet-based L/sub /spl infin//-constrained embedded coding, the bit-stream is truncated at the bit-rate that corresponds to a guaranteed, user-defined distortion bound. The letter analyzes the optimality of embedded deadzone Scalar-Quantizers for high-rate L/sub /spl infin//-constrained scalable wavelet-based image coding. A rate-distortion model applicable to the family of embedded deadzone Scalar-Quantizers is derived and experimentally validated. Conclusions are drawn regarding the optimal subband-quantizer instantiations. The optimal Quantizers are employed in a coding algorithm that retains the coding performance and the flexibility options of wavelet-based codecs while allowing for a fully embedded L/sub /spl infin//-oriented bit-stream.

Michelle Effros - One of the best experts on this subject based on the ideXlab platform.

Related terms

Scalar Quantizers - 15 days free trial to Access Experts & Abstracts