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103
Sigmadelta quantization and finite frames
 in Proc. Int. Conf. Acoustics, Speech and Signal Processing
, 2004
"... Abstract—Thelevel Sigma–Delta () scheme with step size is introduced as a technique for quantizing finite frame expansions for. Error estimates for various quantized frame expansions are derived, and, in particular, it is shown that quantization of a unitnorm finite frame expansion in achieves ap ..."
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Cited by 42 (6 self)
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Abstract—Thelevel Sigma–Delta () scheme with step size is introduced as a technique for quantizing finite frame expansions for. Error estimates for various quantized frame expansions are derived, and, in particular, it is shown that quantization of a unitnorm finite frame expansion in achieves approximation error 2 ( ( ) + 1) where is the frame size, and the frame variation ( ) is a quantity which reflects the dependence of the scheme on the frame. Here is thedimensional Euclidean 2norm. Lower bounds and refined upper bounds are derived for certain specific cases. As a direct consequence of these error bounds one is able to bound the mean squared error (MSE) by an order of 1 2. When dealing with sufficiently redundant frame expansions, this represents a significant improvement over classical pulsecode modulation (PCM) quantization, which only has MSE of order1 under certain nonrigorous statistical assumptions. also achieves the optimal MSE order for PCM with consistent reconstruction. Index Terms—Finite frames, Sigma–Delta quantization. I.
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 pr ..."
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Cited by 41 (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...
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 37 (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.
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 dist ..."
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Cited by 36 (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...
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 multidimensio ..."
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Cited by 35 (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 25 (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 Signal Processing
, 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 20 (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.