Results 1  10
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48
On Lattice Quantization Noise
 IEEE Trans. Inform. Theory
, 1996
"... Abstract We present several results regarding the properties of a random vector, uniformly distributed over a lattice cell. This random vector is the quantization noise of a lattice quantizer at high resolution, or the noise of a dithered lattice quantizer at all distortion levels. We find that for ..."
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Cited by 73 (20 self)
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Abstract We present several results regarding the properties of a random vector, uniformly distributed over a lattice cell. This random vector is the quantization noise of a lattice quantizer at high resolution, or the noise of a dithered lattice quantizer at all distortion levels. We find that for the optimal lattice quantizers this noise is widesensestationary and white. Any desirable noise spectra may be realized by an appropriate linear transformation (“shaping”) of a lattice quantizer. As the dimension increases, the normalized second.moment of the optimal lattice quantizer goes to 1/2xe, and consequently the quantization noise approaches a white Gaussian process in the divergence sense. In entropycoded dithered quantization, which can be modeled accurately as passing the source through an additive noise channel, this limit behavior implies that for large lattice dimension both the error and the bit rate approach the error and the information rate of an Additive White Gaussian Noise (AWGN) channel. Index TermsLattice, quantization noise, shaping, normalized second moment, divergence from Gaussianity. I I.
Statistical Theory of Quantization
 IEEE Trans. on Instrumentation and Measurement
, 1995
"... The effect of uniform quantization can often be modeled by an additive noise that is uniformly distributed, uncorrelated with the input signal, and has a white spectrum. This paper surveys the theory behind this model, and discusses the conditions of its validity. The application of the model to flo ..."
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Cited by 38 (3 self)
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The effect of uniform quantization can often be modeled by an additive noise that is uniformly distributed, uncorrelated with the input signal, and has a white spectrum. This paper surveys the theory behind this model, and discusses the conditions of its validity. The application of the model to floatingpoint quantization is demonstrated. Keywords  Quantization, noise model, quantization noise, noise spectrum, statistical theory, finite bit number, roundoff error, arithmetic rounding, floatingpoint quantization.
Bennett's Integral for Vector Quantizers
 IEEE Trans. Inform. Theory
, 1995
"... This paper extends Bennett's integral from scalar to vector quantizers, giving a simple formula that expresses the rthpower distortion of a manypoint vector quantizer in terms of the number of points, point density function, inertial profile and the distribution of the source. The inertial profile ..."
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Cited by 32 (6 self)
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This paper extends Bennett's integral from scalar to vector quantizers, giving a simple formula that expresses the rthpower distortion of a manypoint vector quantizer in terms of the number of points, point density function, inertial profile and the distribution of the source. The inertial profile specifies the normalized moment of inertia of quantization cells as a function of location. The extension is formulated in terms of a sequence of quantizers whose point density and inertial profile approach known functions as the number of points increases. Precise conditions are given for the convergence of distortion (suitably normalized) to Bennett's integral. Previous extensions did not include the inertial profile and, consequently, provided only bounds or applied only to quantizers with congruent cells, such as lattice and optimal quantizers. The new version of Bennett's integral provides a framework for the analysis of suboptimal structured vector quantizers. It is shown how the loss...
Asymptotic Performance of Vector Quantizers with a Perceptual Distortion Measure
 in Proc. IEEE Int. Symp. on Information Theory, p. 55
, 1997
"... Gersho's bounds on the asymptotic performance of vector quantizers are valid for vector distortions which are powers of the Euclidean norm. Yamada, Tazaki and Gray generalized the results to distortion measures that are increasing functions of the norm of their argument. In both cases, the distortio ..."
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Cited by 28 (3 self)
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Gersho's bounds on the asymptotic performance of vector quantizers are valid for vector distortions which are powers of the Euclidean norm. Yamada, Tazaki and Gray generalized the results to distortion measures that are increasing functions of the norm of their argument. In both cases, the distortion is uniquely determined by the vector quantization error, i.e., the Euclidean difference between the original vector and the codeword into which it is quantized. We generalize these asymptotic bounds to inputweighted quadratic distortion measures, a class of distortion measure often used for perceptually meaningful distortion. The generalization involves a more rigorous derivation of a fixed rate result of Gardner and Rao and a new result for variable rate codes. We also consider the problem of source mismatch, where the quantizer is designed using a probability density different from the true source density. The resulting asymptotic performance in terms of distortion increase in dB is shown...
Sigmadelta quantization and finite frames
 IEEE Trans. Inform. Theory
, 2006
"... It is shown that SigmaDelta (Σ∆) algorithms can be used effectively to quantize finite frame expansions for R d. Error estimates for various quantized frame expansions are derived, and in particular, it is shown that Σ ∆ quantizers outperform the standard PCM schemes. 1. ..."
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Cited by 27 (3 self)
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It is shown that SigmaDelta (Σ∆) algorithms can be used effectively to quantize finite frame expansions for R d. Error estimates for various quantized frame expansions are derived, and in particular, it is shown that Σ ∆ quantizers outperform the standard PCM schemes. 1.
A CMOS Area Image Sensor With Pixel Level A/D Conversion
 IN ISSCC DIGEST OF TECHNICAL PAPERS
, 1995
"... A CMOS 64 x 64 pixel area image sensor chip using SigmaDelta modulation at each pixel for A/D conversion is described. The image data output is digital. The chip was fabricated using a 1.2µm two layer metal single layer poly nwell CMOS process. Each pixel block consists of a phototransistor and ..."
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Cited by 26 (7 self)
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A CMOS 64 x 64 pixel area image sensor chip using SigmaDelta modulation at each pixel for A/D conversion is described. The image data output is digital. The chip was fabricated using a 1.2µm two layer metal single layer poly nwell CMOS process. Each pixel block consists of a phototransistor and 22 MOS transistors. Test results demonstrate a dynamic range potentially greater than 93dB, a signal to noise ratio (SNR) of up to 61dB, and dissipation of less than 1mW with a 5V power supply.
HighResolution Source Coding for NonDifference Distortion Measures: Multidimensional Companding
 IEEE Trans. Inform. Theory
, 1999
"... Entropycoded vector quantization is studied using highresolution multidimensional companding over a class of nondifference distortion measures. For distortion measures which are "locally quadratic" a rigorous derivation of the asymptotic distortion and entropycoded rate of multidimensional compan ..."
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Cited by 22 (3 self)
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Entropycoded vector quantization is studied using highresolution multidimensional companding over a class of nondifference distortion measures. For distortion measures which are "locally quadratic" a rigorous derivation of the asymptotic distortion and entropycoded rate of multidimensional companders is given along with conditions for the optimal choice of the compressor function. This optimum compressor, when it exists, depends on the distortion measure but not on the source distribution. The ratedistortion performance of the companding scheme is studied using a recently obtained asymptotic expression for the ratedistortion function which parallels the Shannon lower bound for difference distortion measures. It is proved that the highresolution performance of the scheme is arbitrarily close to the ratedistortion limit for large quantizer dimensions if the compressor function and the lattice quantizer used in the companding scheme are optimal, extending an analogous statement for...
Asymptotic Analysis of Optimal FixedRate Uniform Scalar Quantization
 IEEE Trans. Inform. Theory
, 2000
"... This paper studies the asymptotic characteristics of uniform scalar quantizers that are optimal with respect to mean squared error. It is shown that when a symmetric source density with infinite support is sufficiently well behaved, the optimal step size D N for symmetric uniform scalar quantization ..."
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Cited by 18 (4 self)
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This paper studies the asymptotic characteristics of uniform scalar quantizers that are optimal with respect to mean squared error. It is shown that when a symmetric source density with infinite support is sufficiently well behaved, the optimal step size D N for symmetric uniform scalar quantization decreases as 2s N 1 V 1 1/6N 2 () , where N is the number of quantization levels, s 2 is the source variance and V 1 () is the inverse of V (y) = y 1 P(s 1 X > x)dx y . Equivalently, the optimal support length ND N increases as 2s V 1 1/6N 2 () . Granular distortion is asymptotically well approximated by D N 2 /12, and the ratio of overload to granular distortion converges to a function of the limit t lim y y 1 E[X X > y], provided, as usually happens, that t exists. When it does, its value is related to the number of finite moments of the source density; an asymptotic formula for the overall distortion D N is obtained; and t = 1 is both necessary...
Highrate quantization and transform coding with side information at the decoder
 EURASIP  Journal on Applied Signal Processing (Special Issue on Distributed Source Coding
, 2006
"... We extend highrate quantization theory to WynerZiv coding, i.e., lossy source coding with side information at the decoder. Ideal SlepianWolf coders are assumed, thus rates are conditional entropies of quantization indices given the side information. This theory is applied to the analysis of ortho ..."
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Cited by 16 (1 self)
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We extend highrate quantization theory to WynerZiv coding, i.e., lossy source coding with side information at the decoder. Ideal SlepianWolf coders are assumed, thus rates are conditional entropies of quantization indices given the side information. This theory is applied to the analysis of orthonormal block transforms for WynerZiv coding. A formula for the optimal rate allocation and an approximation to the optimal transform are derived. The case of noisy highrate quantization and transform coding is included in our study, in which a noisy observation of source data is available at the encoder, but we are interested in estimating the unseen data at the decoder, with the help of side information. We implement a transformdomain WynerZiv video coder that encodes frames independently but decodes them conditionally. Experimental results show that using the discrete cosine transform results in a ratedistortion improvement with respect to the pixeldomain coder. Transform coders of noisy images for different communication constraints are compared. Experimental results show that the noisy WynerZiv transform coder achieves a performance close to the case in which the side information is also available at the encoder. Keywords: highrate quantization, transform coding, side information, WynerZiv coding, distributed source coding, noisy source coding 1.