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http://hdl.handle.net/10397/296
| 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. 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. In most cases, these works may not be reposted without the explicit permission of the copyright holder. |
| Appears in Collections: | Journal/Magazine Article |
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