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Article
Signal analysis using a multiresolution form of the singular value decomposition
Faculty of Informatics - Papers (Archive)
  • Ramakrishna Kakarala, Motorola Australian Research Centre
  • Philip Ogunbona, University of Wollongong
RIS ID
16166
Publication Date
1-1-2001
Publication Details

Kakarala, R. & Ogunbona, P. (2001). Signal analysis using a multiresolution form of the singular value decomposition. IEEE Transactions on Image Processing, 10 (5), 724-735.

Abstract
This paper proposes a multiresolution form of the singular value decomposition (SVD) and shows how it may be used for signal analysis and approximation. It is well-known that the SVD has optimal decorrelation and subrank approximation properties. The multiresolution form of SVD proposed here retains those properties, and moreover, has linear computational complexity. By using the multiresolution SVD, the following important characteristics of a signal may be measured, at each of several levels of resolution: isotropy, sphericity of principal components, self-similarity under scaling, and resolution of mean-squared error into meaningful components. Theoretical calculations are provided for simple statistical models to show what might be expected. Results are provided with real images to show the usefulness of the SVD decomposition.
Citation Information
Ramakrishna Kakarala and Philip Ogunbona. "Signal analysis using a multiresolution form of the singular value decomposition" (2001) p. 724 - 735
Available at: http://works.bepress.com/p_ogunbona/19/