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Title: An efficient computational scheme for the two-dimensional overcomplete wavelet transform
Authors: Law, NFB 
Siu, WC 
Issue Date: Nov-2002
Source: IEEE transactions on signal processing, Nov. 2002, v. 50, no. 11, p. 2806-2819
Abstract: We have studied the computational complexity associated with the overcomplete wavelet transform for the commonly used Spline wavelet family. By deriving general expressions for the computational complexity using the conventional filtering implementation, we show that the inverse transform is significantly more costly in computation than the forward transform. To reduce this computational complexity, we propose a new spatial implementation based on the exploitation of the correlation between the lowpass and the bandpass outputs that is inherent in the overcomplete representation. Both theoretical studies and experimental findings show that the proposed spatial implementation can greatly simplify the computations associated with the inverse transform. In particular, the complexity of the inverse transform using the proposed implementation can be reduced to slightly less than that of the forward transform using the conventional filtering implementation. We also demonstrate that the proposed scheme allows the use of an arbitrary boundary extension method while maintaining the ease of the inverse transform.
Keywords: Computational complexity
Over-complete wavelets
Spatial implementation
Wavelet transform
Publisher: Institute of Electrical and Electronics Engineers
Journal: IEEE transactions on signal processing 
ISSN: 1053-587X
EISSN: 1941-0476
DOI: 10.1109/TSP.2002.804094
Rights: © 2002 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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