A Generalized Lloyd-Type Algorithm for Adaptive Transform Coder Design

Cynthia Archer, Todd K. Leen

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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
Issue number1
StatePublished - Jan 2004
Externally publishedYes


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

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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