Optimality of KLT for High-Rate Transform Coding of Gaussian Vector-Scale Mixtures: Application to Reconstruction, Estimation, and Classification

Jana, Soumya; Moulin, Pierre

doi:10.1109/tit.2006.880056

Cited by 21 publications

(28 citation statements)

References 55 publications

(61 reference statements)

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“…Specifically, there is a family of distributions where KLT has been shown to be optimal for transform coding although it does not generate independent coefficients [6].…”

Section: On Optimality Of Kltmentioning

confidence: 99%

“…Jana-Moulin (JM) Theorem [6]: KLT is optimal for a GVSM source for variable rate coding at high resolution.…”

Section: On Optimality Of Kltmentioning

confidence: 99%

“…In [6], a significant positive result is obtained regarding the optimality of KLT: KLT is optimal in conjunction with variable rate high resolution coding, not only for Gaussians but for the broader family of Gaussian vector mixtures, which includes Gaussian mixture models.…”

Section: Introductionmentioning

confidence: 99%

“…This suggests that advances in transform coding may have an impact directly in source separation. An example of such a result is presented in Section IV, where our necessary and sufficient condition for optimality maps the result of [6] to ensure the optimality of KLT for source separation of Gaussian vector mixtures.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Specifically, there is a family of distributions where KLT has been shown to be optimal for transform coding although it does not generate independent coefficients [6].…”

Section: On Optimality Of Kltmentioning

confidence: 99%

“…Jana-Moulin (JM) Theorem [6]: KLT is optimal for a GVSM source for variable rate coding at high resolution.…”

Section: On Optimality Of Kltmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…In another useful reference [18], optimal transform coding of Gaussian vector scale mixtures, which include GG sources as particular cases, was studied at high bitrate, for 1 For simplicity, the entropies will be expressed in Nats.…”

Section: Introductionmentioning

confidence: 99%

On the Uniform Quantization of a Class of Sparse Sources

Fraysse

Pesquet‐Popescu

Pesquet

2009

IEEE Trans. Inform. Theory

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We consider the uniform scalar quantization of a class of mixed distributed memoryless sources, namely sources having a Bernoulli-Generalized Gaussian distribution. Both for low and high resolutions, asymptotic expressions of the distortion for a p-th order moment error measure, and close approximations of the entropy are provided for these sources. Operational rate-distortion functions at high bitrate and their slope factors at low bitrate are derived. The dependence of these results on p and the distribution parameters as well as the relation to the Shannon optimal rate-distortion bound are then discussed.

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Dictionary-based monitoring of premature ventricular contractions: An ultra-low-cost point-of-care service

Bollepalli

Challa

Anumandla³

et al. 2018

Artificial Intelligence in Medicine

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While cardiovascular diseases (CVDs) are prevalent across economic strata, the economically disadvantaged population is disproportionately affected due to the high cost of traditional CVD management, involving consultations, testing and monitoring at medical facilities. Accordingly, developing an ultra-low-cost alternative, affordable even to groups at the bottom of the economic pyramid, has emerged as a societal imperative. Against this backdrop, we propose an inexpensive yet accurate home-based electrocardiogram (ECG) monitoring service. Specifically, we seek to provide point-of-care monitoring of premature ventricular contractions (PVCs), high frequency of which could indicate the onset of potentially fatal arrhythmia. Note that the first-generation telecardiology system acquires the ECG, transmits it to a professional diagnostic center without processing, and nearly achieves the diagnostic accuracy of a bedside setup. In the process, such a system incurs high bandwidth cost and requires the physicians to process the entire record for diagnosis. To reduce cost, current telecardiology systems compress data before transmitting. However, the burden on physicians remains undiminished. In this context, we develop a dictionary-based algorithm that reduces not only the overall bandwidth requirement, but also the physicians workload by localizing anomalous beats. Specifically, we detect anomalous beats with high sensitivity and only those beats are then transmitted. In fact, we further compress those beats using class-specific dictionaries subject to suitable reconstruction/diagnostic fidelity. Finally, using Monte Carlo cross validation on MIT/BIH arrhythmia database, we evaluate the performance of the proposed system. In particular, with a sensitivity target of at most one undetected PVC in one hundred beats, and a percentage root mean squared difference less than 9% (a clinically acceptable level of fidelity), we achieved about 99.15% reduction in bandwidth cost, equivalent to 118-fold savings over first-generation telecardiology. In the process, the professional workload is reduced by at least 85.9% for noncritical cases. Our algorithm also outperforms known algorithms under certain measures in the telecardiological context.

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Optimality of KLT for High-Rate Transform Coding of Gaussian Vector-Scale Mixtures: Application to Reconstruction, Estimation, and Classification

Cited by 21 publications

References 55 publications

A necessary and sufficient condition for transform optimality in source coding

A necessary and sufficient condition for transform optimality in source coding

On the Uniform Quantization of a Class of Sparse Sources

Dictionary-based monitoring of premature ventricular contractions: An ultra-low-cost point-of-care service

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