Convex multiresolution analysis
A standard wavelet multiresolution analysis can be defined via a sequence of projectors onto a monotone sequence of closed vector subspaces possessing certain properties. We propose a nonlinear extension of this framework in which the vector subspaces are replaced by convex subsets. These sets are c...
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Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence 1998-12, Vol.20 (12), p.1308-1318 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | A standard wavelet multiresolution analysis can be defined via a sequence of projectors onto a monotone sequence of closed vector subspaces possessing certain properties. We propose a nonlinear extension of this framework in which the vector subspaces are replaced by convex subsets. These sets are chosen so as to provide a recursive, monotone approximation scheme that allows for various signal and image features to be investigated. Several classes of convex multiresolution analyses are discussed and numerical applications to signal and image-processing problems are demonstrated. |
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ISSN: | 0162-8828 1939-3539 |
DOI: | 10.1109/34.735804 |