F. Mendivil, D. Piché. Two algorithms for non-separable wavelet transforms and applications to image compression. In Fractals: Theory and Applications in Engineering, M. Dekking, J. L. Vehel, E. Lutton, C. Tricot (eds.), pp. 325-345, Springer-Verlag, London, 1999.
Previously, the use of non-separable wavelets in image processing has been hindered by the lack of a fast algorithm to perform a non-separable wavelet transform. We present two such algorithms in this paper. The first algorithm implements a periodic wavelet transform for any valid wavelet filter sequence and dilation matrices satisfying a trace condition. We disduss some of the complicating issues unique to the non-separable case and how to overcome them. The second algorithm links Haar wavelets and complex bases and uses this link to drive the algorithm. For the complex bases case, the asymmetry of the wavelet trees produced leads to a discussionof the complexities in implementing zero-tree and other wavelet compression methods. We describe some preliminary attempts at using this algorithm, with non-separable Haar wavelets, for reducing the blocking artifacts in fractal image compression.
Download paper:
Adobe PDF
Copyright notice: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.
@InCollection{MePi99,
Author = {Mendivil, F. and Piché, D.},
Title = {Two algorithms for non-separable wavelet transforms and applications to image compression},
BookTitle = {Fractals: Theory and Applications in Engineering},
editor = {Dekking, M. and Vehel, J. L. and Lutton, E. and Tricot, C.},
Pages = {325--345},
Publisher = {Springer-Verlag},
Address = {London},
Year = {1999}
}