A Generalized Lloyd-Type Algorithm for Adaptive Transform Coder Design

Archer, Cynthia; Leen, Todd K.

doi:10.1109/tsp.2003.819980

Cited by 19 publications

(23 citation statements)

References 15 publications

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“…Especially in [16], the transform matrices found by a new algorithm outperform the KLT by 0.3 to 1.2 dB on benchmark images like "Barbara" and "Goldhill." When the impact of the lack of stationarity in the source is reduced by using adaptive coding, the performance of the KLT is about 0.4-1 dB worse.…”

Section: Discussionmentioning

confidence: 98%

“…For real sources, some experimental results on the suboptimality of the KLT have been reported in [5] and [16]. Especially in [16], the transform matrices found by a new algorithm outperform the KLT by 0.3 to 1.2 dB on benchmark images like "Barbara" and "Goldhill."…”

Section: Discussionmentioning

confidence: 99%

“…There are two possible ways to pursue a truly optimal transform in variable-rate coding: we can either minimize the sum of the transformed component's entropy as (2) suggests, or minimize the distortion directly for a particular probabilistic model (e.g., the GMM model) as done in [16].…”

Section: Discussionmentioning

confidence: 99%

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Suboptimality of the Karhunen–LoÈve Transform for Transform Coding

Effros

Feng

Zeger

2004

IEEE Trans. Inform. Theory

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Abstract-We examine the performance of the Karhunen-Loève transform (KLT) for transform coding applications. The KLT has long been viewed as the best available block transform for a system that orthogonally transforms a vector source, scalar quantizes the components of the transformed vector using optimal bit allocation, and then inverse transforms the vector. This paper treats fixed-rate and variable-rate transform codes of non-Gaussian sources. The fixed-rate approach uses an optimal fixed-rate scalar quantizer to describe the transform coefficients; the variable-rate approach uses a uniform scalar quantizer followed by an optimal entropy code, and each quantized component is encoded separately. Earlier work shows that for the variable-rate case there exist sources on which the KLT is not unique and the optimal quantization and coding stage matched to a "worst" KLT yields performance as much as 1.5 dB worse than the optimal quantization and coding stage matched to a "best" KLT. In this paper, we strengthen that result to show that in both the fixed-rate and the variable-rate coding frameworks there exist sources for which the performance penalty for using a "worst" KLT can be made arbitrarily large. Further, we demonstrate in both frameworks that there exist sources for which even a best KLT gives suboptimal performance. Finally, we show that even for vector sources where the KLT yields independent coefficients, the KLT can be suboptimal for fixed-rate coding.

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Section: Discussionmentioning

confidence: 98%

Section: Discussionmentioning

confidence: 99%

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Suboptimality of the Karhunen–LoÈve Transform for Transform Coding

Effros

Feng

Zeger

2004

IEEE Trans. Inform. Theory

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“…The problem is approached from a more practical perspective of numerical design in [7]. The authors proposed a gradient descent iterative algorithm to optimize the optimal orthogonal transform in conjunction with optimization of the quantization scheme.…”

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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“…Particularly, in the so-called lossy transform/subband coding techniques [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], original signal data are transformed to a vector source, that is, a set of coefficients. Then each coefficient is quantized to a symbol which is encoded using certain number of bits.…”

Section: Introductionmentioning

confidence: 99%

On Optimal Bit Allocation for Classification‐Based Source‐Dependent Transform Coding

Akopian

2008

Journal of Electrical and Computer Engineering

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An optimal bit allocation is presented for classification-based source-dependent transform coding. A vector of transform coefficients is considered to have been produced by a mixture of processes. The available bit resource is distributed optimally in two stages: (1) bit allocation is performed for each class of coefficient vectors, and (2) bit allocation is performed for each vector coefficient. The solution for low bit rates imposing nonnegative bit resource is also presented. The rate-distortion bound of the classification-based source coding is derived.

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A Generalized Lloyd-Type Algorithm for Adaptive Transform Coder Design

Cited by 19 publications

References 15 publications

Suboptimality of the Karhunen–LoÈve Transform for Transform Coding

Suboptimality of the Karhunen–LoÈve Transform for Transform Coding

A necessary and sufficient condition for transform optimality in source coding

On Optimal Bit Allocation for Classification‐Based Source‐Dependent Transform Coding

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