Block Quantization of Correlated Gaussian Random Variables

Huang, Jingwei; Schultheiss, P.M.

doi:10.1109/tcom.1963.1088759

Cited by 328 publications

(197 citation statements)

References 3 publications

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“…We will compare MSE and the Rate-Distortion performance of our proposed quantizers based on the first scheme with optimal quantization lattices, the unrestricted polar quantizers [14] (indicated by 'UPQ'), the restricted polar quantizers [11] (indicated by 'PQ'), the rectangular quantizers [6] (indicated by 'Rectangular'). The rate here is defined as log 2 N/2.…”

Section: Resultsmentioning

confidence: 99%

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Approximating vector quantisation by transformation and scalar quantisation

Yang¹,

Hao²,

Wu³

2014

IET Communications

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Abstract-Vector quantization provides better ratedistortion performance over scalar quantization even for a random vector with independent dimensions. However, the design and implementation complexity of vector quantizers is much higher than that of scalar quantizers. To reduce the complexity while achieving performance close to optimal vector quantization and better than scalar quantization, we propose a new quantization scheme, which consists of a transformation and scalar quantization. The transformation is to convert a two-axis representation to a triaxis representation; then scalar quantization is applied to each of the three axes. The proposed quantizer is asymptotically optimal/suboptimal for low/high rate quantization, especially for the quantization with certain prime number of quantization levels. The proposed quantizer has O(N 2 ) design complexity, while VQ has O(N !) design complexity, where N is the number of quantization levels per dimension. The experimental results show that it achieves average bit-rate saving of 0.4%-24.5% over restricted/unrestricted polar quantizers and rectangular quantizers for signals of circular and elliptical Gaussian distributions and Laplace distributions. It holds potential of improving the performance of existing image and video coding schemes.

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Section: Resultsmentioning

confidence: 99%

“…Schultheiss's method [6], which quantizes each dimension of random variables in Gaussian distributions with separate one-dimensional Lloyd-Max quantizers [7]. It is efficient and effective, but definitely could be improved.…”

Section: Introductionmentioning

confidence: 99%

Approximating vector quantisation by transformation and scalar quantisation

Yang¹,

Hao²,

Wu³

2014

IET Communications

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“…The bits allocated to represent them must be assigned to each coefficient according to a bit allocation scheme. The classical bit allocation scheme is based on reports by Huang and Schultheiss (1963) and Segall (1976). The goal of bit allocation is to minimize the overall mean square error in the reconstructed image given a limited number of bits with which to represent the transformed image.…”

Section: Holographic Quantization Of Transform Coefficientsmentioning

confidence: 99%

“…The goal of bit allocation is to minimize the overall mean square error in the reconstructed image given a limited number of bits with which to represent the transformed image. One method (Huang and Schultheiss, 1963;Segall, 1976), which is described below, assumes that the total number of bits is fixed and seeks to minimize the total error by determining to which random variable subsequent bits should be assigned, until that number of bits has been assigned. Another approach is provided by Bruckstein (1987), who reported that the user has the option to strike a balance between the total quantization error and the number of bits used.…”

Section: Holographic Quantization Of Transform Coefficientsmentioning

confidence: 99%

On holographic transform compression of images

Bruckstein¹,

Holt²,

Netravali³

2000

Int J Imaging Syst Tech

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Lossy transform compression of images is successful and widespread. The JPEG standard uses the discrete cosine transform on blocks of the image and a bit allocation process that takes advantage of the uneven energy distribution in the transform domain. For most images, 10:1 compression ratios can be achieved with no visible degradations. However, suppose that multiple versions of the compressed image exist in a distributed environment such as the internet, and several of them could be made available upon request. The classical approach would provide no improvement in the image quality if more than one version of the compressed image became available. In this paper, we propose a method, based on multiple description scalar quantization, that yields decompressed image quality that improves with the number of compressed versions available.

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“…In their seminal paper, Huang and Schulthesis have shown [3] that if the vector source is Gaussian and the bit budget is asymptotically large, then the Karhunen Loeve transform (KLT) and its inverse are an optimal pair of transforms for fixed-rate coding. In a more recent paper Goyal, Zhuang and Vetterli improve that result by showing that KLT is optimal for Gaussian This work is supported in part by the NSF under grants CCF-0728986 and CCF-1016861 sources without making any high resolution assumptions [4].…”

Section: Introductionmentioning

confidence: 99%

A necessary and sufficient condition for transform optimality in source coding

Akyol

Rose

2011

2011 IEEE International Symposium on Information Theory Proceedings

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Abstract-It is well-known for transform coding of multivariate Gaussian sources, that the Karhunen Loeve transform (KLT) minimizes the mean square error distortion. However, finding the optimal transform for general non-Gaussian sources has been an open problem for decades, despite several important advances that provide some partial answers regarding KLT optimality. In this paper, we present a necessary and sufficient condition for optimality of a transform when high resolution, variable rate quantizers are employed. We present not only a complete characterization of when KLT is optimal, but also a determining condition for optimality of a general (non-KLT) transform. This necessary and sufficient condition is shown to have direct connections to the well studied source separation problem. This observation can impact source separation itself, as illustrated with a new optimality result. Finally, we combine the transform optimality condition with algorithmic tools from source separation, to derive a practical numerical method to search for the optimal transform in source coding.

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Block Quantization of Correlated Gaussian Random Variables

Cited by 328 publications

References 3 publications

Approximating vector quantisation by transformation and scalar quantisation

Approximating vector quantisation by transformation and scalar quantisation

On holographic transform compression of images

A necessary and sufficient condition for transform optimality in source coding

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