P. Elias, "Bounds on performance of optimum quantizers," IEEE Trans. Inform. Theory, vol. 16, pp. 172--184, March 1970.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... of properties of optimal high resolution quantization for both fixed and variable rate quantization for squared error and other error moments appeared during the 1960 s, e.g. 497] 498] 55] 467] 8] An excellent summary of the early work is contained in a 1970 paper by Elias [143]. We close this section with an important practical observation. The current JPEG and related standards can be viewed as a combination of transform coding and variablelength quantization. It is worth pointing out how the standard resembles and di#ers from the models considered thus far. As ....

....1,1 (R) Z 1,1 (R) # 1asR##. But as to the details it o#ered only that: The complete proof is surprisingly long and will not be given here. Though Gish and Pierce were the first to informally derive (13) neither this paper nor any paper to date has provided a rigorous derivation. Elias (1970) [143] also made a rigorous analysis of scalar quantization, giving asymptotic bounds to the distortion of scalar quantizers with a rather singularly defined measure of distortion, namely, the rth root of the average of the rth power of the cell widths. A companion paper [144] considers similar bounds ....

P. Elias, "Bounds on performance of optimum quantizers," IEEE Trans. Inform. Theory, vol. 16, pp. 172--184, March 1970.

.... of properties of optimal high resolution quantization for both fixed and variable rate quantization for squared error and other error moments appeared during the 1960 s, e.g. 497] 498] 55] 467] 8] An excellent summary of the early work is contained in a 1970 paper by Elias [143]. We close this section with an important practical observation. The current JPEG and related standards can be viewed as a combination of transform coding and variablelength quantization. It is worth pointing out how the standard resembles and differs from the models considered thus far. As ....

....(R) Z 1;1 (R) 1 as R 1. But as to the details it offered only that: The complete proof is surprisingly long and will not be given here. Though Gish and Pierce were the first to informally derive (13) neither this paper nor any paper to date has provided a rigorous derivation. Elias (1970) [143] also made a rigorous analysis of scalar quantization, giving asymptotic bounds to the distortion of scalar quantizers with a rather singularly defined measure of distortion, namely, the rth root of the average of the rth power of the cell widths. A companion paper [144] considers similar bounds ....

P. Elias, "Bounds on performance of optimum quantizers," IEEE Trans. Inform. Theory, vol. 16, pp. 172--184, March 1970.

.... the characterizations of properties of optimal high resolution quantization for both fixed and variable rate quantization for squared error and other error moments appeared during the 1960s, e.g. 350, 351, 45, 330, 6] An excellent summary of the early work is contained in a 1970 paper by Elias [110]. We now momentarily leave the discussion of variable rate scalar quantization to discuss one of the first vector quantizers since this early example provided the vehicle for the development of optimal varible rate scalar quantizers. In 1965 Dunn [106] introduced a form of vector quantization for ....

....(R) Z 1;1 (R) 1 as R 1. But as to the details it offered only that: The complete proof is surprisingly long and will not be given here. Though Gish and Pierce were the first to informally derive (29) neither this paper nor any paper to date has provided a rigorous derivation. Elias (1970) [110] also made a rigorous analysis of scalar quantization, giving asymptotic bounds to the distortion of scalar quantizers with a rather singularly defined measure of distortion, namely, the rth root of the average of the rth power of the cell widths. A companion paper [111] considers similar bounds ....

P. Elias, "Bounds on performance of optimum quantizers," IEEE Trans. Information Theory, Vol. 16, pp. 172-184, March 1970.

....purpose of analog to digital conversion in signal processing. In the methods described in the literature, instead of quantizing a discrete variable using frequency histograms, one quantizes over a continuous range whose statistics are given by the probability density of a random variable. Elias [12] gives an excellent history of the subject. Max [30] was one of the first to write about the subject of optimal quantization. His method was to approximate the probability density of an analog signal with a gaussian distribution, find the optimal quantizer for the gaussian, and use that quantizer ....

Elias, P., "Bounds on Performance of Optimum Quantizers," IEEE Trans. on Information Theory, Vol. IT-16, No. 2, March 1970.

....technical conditions, a form of Bennett s integral holds, whenever the sequence of quantizers is asymptotically optimum for some other source density. Over the years, other work has focused on deriving the asymptotically best performance of quantizers without explicit use of Bennett s integral [13 19]. A thorough summary of early work is contained in [19] A complete extension of Bennett s integral to vector quantizers must take into account the shape of the quantization cells and, indeed, the possibility that in two or more dimensions the cells may have many different shapes. In the following ....

....whenever the sequence of quantizers is asymptotically optimum for some other source density. Over the years, other work has focused on deriving the asymptotically best performance of quantizers without explicit use of Bennett s integral [13 19] A thorough summary of early work is contained in [19]. A complete extension of Bennett s integral to vector quantizers must take into account the shape of the quantization cells and, indeed, the possibility that in two or more dimensions the cells may have many different shapes. In the following we give a heuristic derivation of our extension of ....

P. Elias, "Bounds on performance of optimum quantizers," IEEE Trans. Inform. Theory, vol. IT-16, pp. 172-184, March 1970.

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P. Elias, "Bounds on performance of optimum quantizers," IEEE Trans. Inform. Theory, vol. IT-16, pp. 172-184, March 1970.

No context found.

P. Elias, Bounds on performance of optimum quantizers," IEEE Trans. on Inform. Theory, vol. IT-16, pp. 172-184, March 1970.

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