MATHEMATICAL IMAGING

Wavelet decomposition/reconstruction of images via direct products

[+] Author Affiliations
Ronald G. Spencer

Texas A&M University, Department of Electrical Engineering, College Station, Texas?77843

J. Electron. Imaging. 9(1), 61-71 (Jan 01, 2000). doi:10.1117/1.482726
History: Received Nov. 18, 1998; Revised Aug. 25, 1999; Accepted Sep. 24, 1999
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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. © 2000 SPIE and IS&T.

© 2000 SPIE and IS&T

Topics

Wavelets

Citation

N. C. Griswold ; Somit Shah Mathur ; Mark Yeary and Ronald G. Spencer
"Wavelet decomposition/reconstruction of images via direct products", J. Electron. Imaging. 9(1), 61-71 (Jan 01, 2000). ; http://dx.doi.org/10.1117/1.482726


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