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J. Li, N. Chaddha, R. M. Gray, ``Asymptotic performance of vector
quantizers with a perceptual distortion measure,''
IEEE Transactions on
Information Theory, 45(4):1082-91, May 1999.
(download)
Abstract:
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
input-weighted quadratic distortion measures and measures that are
approximately output-weighted quadratic when the distortion is small, a class
of distortion measures often claimed to be perceptually meaningful. An
approximation of the asymptotic distortion based on Gersho's conjecture is
derived as well. We also consider the problem of source mismatch, where the
quantizer is designed using a probability density di erent from the true
source density. The resulting asymptotic performance in terms of distortion
increase in dB is shown to be linear in the relative entropy between the true
and estimated probability densities.
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R. M. Gray, T. Linder, J. Li, ``A lagrangian formulation of Zador's
entropy-constrained quantization theorem,''
IEEE Transactions on Information
Theory, 48(3):695-707, 2002.
(download)
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Jia Li, Robert M. Gray, Richard A. Olshen, "Multiresolution image
classification by hierarchical modeling with two dimensional hidden Markov
models," IEEE Transactions on Information Theory, 46(5):1826-41, August 2000.
Abstract:
This paper treats a multiresolution hidden Markov model for classifying
images. Each image is represented by feature vectors at several resolutions,
which are statistically dependent as modeled by the underlying state process,
a multiscale Markov mesh. Unknowns in the model are estimated by maximum
likelihood, in particular by employing the expectation-maximization
algorithm. An image is classified by finding the optimal set of states with
maximum a posteriori probability. States are then mapped into classes. The
multiresolution model enables multiscale information about context to be
incorporated into classification. Suboptimal algorithms based on the model
provide progressive classification that is much faster than the algorithm
based on single-resolution hidden Markov models.
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