1 January 2000 Wavelet decomposition/reconstruction of images via direct products
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J. of Electronic Imaging, 9(1), (2000). doi:10.1117/1.482726
Abstract
The two major aspects of image data compression utilizing wavelet analysis and synthesis are the decomposition of an image and the reconstruction of this image. It has been noticed in this investigation that the pyramid structure of convolution and the down sampling or the up sampling (adding zeros) and convolution have equivalent operations in vector space analysis. That is, the decomposition is equivalent to an outer product expansion. Therefore, tensor products can easily accomplish the synthesis or reconstruction. This is sometimes called the direct product. It is suggested that this method of implementation saves operations and opens the way to utilization of uniform filter banks.
Norman C. Griswold, Somit Shah Mathur, Mark B. Yeary, Ronald G. Spencer, "Wavelet decomposition/reconstruction of images via direct products," Journal of Electronic Imaging 9(1), (1 January 2000). http://dx.doi.org/10.1117/1.482726
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KEYWORDS
Wavelets

Digital signal processing

Matrices

Image processing

Convolution

Image filtering

Image analysis

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