Signal analysis using a multiresolution form of the singular value decomposition

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...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on image processing 2001-05, Vol.10 (5), p.724-735
Main Authors: Kakarala, R., Ogunbona, P.O.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Australia
Covariance matrix
Decomposition
Decorrelation
Eigenvalues and eigenfunctions
Error analysis
Exact sciences and technology
Information, signal and communications theory
Karhunen-Loeve transforms
Mathematical analysis
Mathematical models
Matrix decomposition
Optimization
Principal component analysis
Signal analysis
Signal and communications theory
Signal representation. Spectral analysis
Signal resolution
Signal, noise
Singular value decomposition
Telecommunications and information theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 he 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.
ISSN:1057-7149
1941-0042
DOI:10.1109/83.918566