A Generalized Lloyd-Type Algorithm for Adaptive Transform Coder Design

Cynthia Archer, Todd K. Leen

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this paper, we establish a probabilistic framework for adaptive transform coding that leads to a generalized Lloyd type algorithm for transform coder design. Transform coders are often constructed by concatenating an ad hoc choice of transform with suboptimal bit allocation and quantizer design. Instead, we start from a probabilistic latent variable model in the form of a mixture of constrained Gaussian mixtures. From this model, we derive an transform coder design algorithm, which integrates optimization of all transform coder parameters. An essential part this algorithm is our introduction of a new transform basis - the coding optimal transform - which, unlike commonly used transforms, minimizes compression distortion. Adaptive transform coders can be effective for compressing databases of related imagery since the high overhead associated with these coders can be amortized over the entire database. For this work, we performed compression experiments on a database of synthetic aperture radar images. Our results show that adaptive coders improve compressed signal-to-noise ratio (SNR) by approximately 0.5 dB compared with global coders. Coders that incorporated the coding optimal transform had the best SNRs on the images used to develop the coder. However, coders that incorporated the discrete cosine transform generalized better to' new images.

Original languageEnglish (US)
Pages (from-to)255-264
Number of pages10
JournalIEEE Transactions on Signal Processing
Volume52
Issue number1
DOIs
StatePublished - Jan 2004

Fingerprint

Mathematical transformations
Discrete cosine transforms
Synthetic aperture radar
Signal to noise ratio
Experiments

Keywords

  • Adaptive transform coding
  • Compression
  • Entropy-constrained quantization
  • Expectation-maximization
  • Gaussian mixtures
  • Generalized Lloyd algorithms

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

A Generalized Lloyd-Type Algorithm for Adaptive Transform Coder Design. / Archer, Cynthia; Leen, Todd K.

In: IEEE Transactions on Signal Processing, Vol. 52, No. 1, 01.2004, p. 255-264.

Research output: Contribution to journalArticle

Archer, Cynthia ; Leen, Todd K. / A Generalized Lloyd-Type Algorithm for Adaptive Transform Coder Design. In: IEEE Transactions on Signal Processing. 2004 ; Vol. 52, No. 1. pp. 255-264.
@article{a15f9b35d84c45fe8343845b00596dec,
title = "A Generalized Lloyd-Type Algorithm for Adaptive Transform Coder Design",
abstract = "In this paper, we establish a probabilistic framework for adaptive transform coding that leads to a generalized Lloyd type algorithm for transform coder design. Transform coders are often constructed by concatenating an ad hoc choice of transform with suboptimal bit allocation and quantizer design. Instead, we start from a probabilistic latent variable model in the form of a mixture of constrained Gaussian mixtures. From this model, we derive an transform coder design algorithm, which integrates optimization of all transform coder parameters. An essential part this algorithm is our introduction of a new transform basis - the coding optimal transform - which, unlike commonly used transforms, minimizes compression distortion. Adaptive transform coders can be effective for compressing databases of related imagery since the high overhead associated with these coders can be amortized over the entire database. For this work, we performed compression experiments on a database of synthetic aperture radar images. Our results show that adaptive coders improve compressed signal-to-noise ratio (SNR) by approximately 0.5 dB compared with global coders. Coders that incorporated the coding optimal transform had the best SNRs on the images used to develop the coder. However, coders that incorporated the discrete cosine transform generalized better to' new images.",
keywords = "Adaptive transform coding, Compression, Entropy-constrained quantization, Expectation-maximization, Gaussian mixtures, Generalized Lloyd algorithms",
author = "Cynthia Archer and Leen, {Todd K.}",
year = "2004",
month = "1",
doi = "10.1109/TSP.2003.819980",
language = "English (US)",
volume = "52",
pages = "255--264",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "1",

}

TY - JOUR

T1 - A Generalized Lloyd-Type Algorithm for Adaptive Transform Coder Design

AU - Archer, Cynthia

AU - Leen, Todd K.

PY - 2004/1

Y1 - 2004/1

N2 - In this paper, we establish a probabilistic framework for adaptive transform coding that leads to a generalized Lloyd type algorithm for transform coder design. Transform coders are often constructed by concatenating an ad hoc choice of transform with suboptimal bit allocation and quantizer design. Instead, we start from a probabilistic latent variable model in the form of a mixture of constrained Gaussian mixtures. From this model, we derive an transform coder design algorithm, which integrates optimization of all transform coder parameters. An essential part this algorithm is our introduction of a new transform basis - the coding optimal transform - which, unlike commonly used transforms, minimizes compression distortion. Adaptive transform coders can be effective for compressing databases of related imagery since the high overhead associated with these coders can be amortized over the entire database. For this work, we performed compression experiments on a database of synthetic aperture radar images. Our results show that adaptive coders improve compressed signal-to-noise ratio (SNR) by approximately 0.5 dB compared with global coders. Coders that incorporated the coding optimal transform had the best SNRs on the images used to develop the coder. However, coders that incorporated the discrete cosine transform generalized better to' new images.

AB - In this paper, we establish a probabilistic framework for adaptive transform coding that leads to a generalized Lloyd type algorithm for transform coder design. Transform coders are often constructed by concatenating an ad hoc choice of transform with suboptimal bit allocation and quantizer design. Instead, we start from a probabilistic latent variable model in the form of a mixture of constrained Gaussian mixtures. From this model, we derive an transform coder design algorithm, which integrates optimization of all transform coder parameters. An essential part this algorithm is our introduction of a new transform basis - the coding optimal transform - which, unlike commonly used transforms, minimizes compression distortion. Adaptive transform coders can be effective for compressing databases of related imagery since the high overhead associated with these coders can be amortized over the entire database. For this work, we performed compression experiments on a database of synthetic aperture radar images. Our results show that adaptive coders improve compressed signal-to-noise ratio (SNR) by approximately 0.5 dB compared with global coders. Coders that incorporated the coding optimal transform had the best SNRs on the images used to develop the coder. However, coders that incorporated the discrete cosine transform generalized better to' new images.

KW - Adaptive transform coding

KW - Compression

KW - Entropy-constrained quantization

KW - Expectation-maximization

KW - Gaussian mixtures

KW - Generalized Lloyd algorithms

UR - http://www.scopus.com/inward/record.url?scp=0347603363&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347603363&partnerID=8YFLogxK

U2 - 10.1109/TSP.2003.819980

DO - 10.1109/TSP.2003.819980

M3 - Article

AN - SCOPUS:0347603363

VL - 52

SP - 255

EP - 264

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 1

ER -