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  • Research Article
  • Open Access

On a Class of Parametric Transforms and Its Application to Image Compression

EURASIP Journal on Advances in Signal Processing20072007:058416

  • Received: 14 July 2006
  • Accepted: 27 April 2007
  • Published:


A class of parametric transforms that are based on unified representation of transform matrices in the form of sparse matrix products is described. Different families of transforms are defined within the introduced class. All transforms of one family can be computed with fast algorithms similar in structure to each other. In particular, the family of Haar-like transforms consists of discrete orthogonal transforms of arbitrary order such that they all may be computed with a fast algorithm that is in structure similar to classical fast Haar transform. A method for parameter selection is proposed that allows synthesizing specific transforms with matrices containing predefined row(s). The potential of the proposed class of Haar-like parametric transforms to improve the performance of fixed block transforms in image compression is investigated. With this purpose, two image compression schemes are proposed where a number of Haar-like transforms are synthesized each adapted to a certain set of blocks within an image.The nature of the proposed schemes is such that their performance (in terms of PSNR versus compression ratio) cannot be worse than a scheme based on classical discrete cosine transform (DCT). Simulations show that a significant performance improvement can be achieved for certain types of images such as medical X-ray images and compound images.


  • Compression Ratio
  • Discrete Cosine Transform
  • Unify Representation
  • Fast Algorithm
  • Matrix Product

Authors’ Affiliations

Institute of Signal Processing, Tampere University of Technology (TUT), P.O. Box 527, Tampere, 33101, Finland
Nokia Research Center, P.O. Box 100, Tampere, 33721, Finland


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© Susanna Minasyan et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.