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Title: A fast and efficient computational structure for the 2D over-complete wavelet transform
Authors: Law, NFB 
Siu, WC 
Issue Date: 2003
Source: 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing : proceedings : April 6-10, 2003, Hong Kong Exhibition and Convention Centre, Hong Kong, p. III309-III312
Abstract: We studied the computational complexity of the over-complete wavelet representation for the commonly used Spline wavelet family with an arbitrary order. By deriving a general expression for the complexity, it is shown that the inverse transform is significantly more costly in computation than the forward transform. In order to reduce the computational complexity, a new spatial implementation is proposed. This new implementation exploits the redundancy between the lowpass and the bandpass outputs that is inherent to the over-complete wavelet scheme. It is shown that the new implementation can greatly simplify the computations, give an efficient inverse structure and allow the use of an arbitrary boundary extension method without affecting the ease of the inverse transform.
Keywords: Wavelet transform
Computational complexity
Publisher: IEEE
ISBN: 0-7803-7663-3
Rights: © 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
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