Nonlinear wavelet image processing : variational problems, compression, and noise removal through wavelet shrinkage
This paper examines the relationship between wavelet-based image processing algorithms and variational problems. Algorithms are derived as exact or approximate minimizers of variational problems; in particular, we show that wavelet shrinkage can be considered the exact minimizer of the following pro...
| Veröffentlicht in: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 7(1998), 3 vom: 30., Seite 319-35 |
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| 1. Verfasser: | |
| Weitere Verfasser: | , , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1998
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
| Schlagworte: | Journal Article |
| Zusammenfassung: | This paper examines the relationship between wavelet-based image processing algorithms and variational problems. Algorithms are derived as exact or approximate minimizers of variational problems; in particular, we show that wavelet shrinkage can be considered the exact minimizer of the following problem. Given an image F defined on a square I, minimize over all g in the Besov space B(1)(1)(L (1)(I)) the functional |F-g|(L2)(I)(2)+lambda|g|(B(1)(1 )(L(1(I)))). We use the theory of nonlinear wavelet image compression in L(2)(I) to derive accurate error bounds for noise removal through wavelet shrinkage applied to images corrupted with i.i.d., mean zero, Gaussian noise. A new signal-to-noise ratio (SNR), which we claim more accurately reflects the visual perception of noise in images, arises in this derivation. We present extensive computations that support the hypothesis that near-optimal shrinkage parameters can be derived if one knows (or can estimate) only two parameters about an image F: the largest alpha for which FinEpsilon(q)(alpha )(L(q)(I)),1/q=alpha/2+1/2, and the norm |F|B(q)(alpha)(L(q)(I)). Both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than Donoho and Johnstone's VisuShrink procedure; an example suggests, however, that Donoho and Johnstone's SureShrink method, which uses a different shrinkage parameter for each dyadic level, achieves a lower error than our procedure |
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| Beschreibung: | Date Completed 15.12.2009 Date Revised 15.02.2008 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1941-0042 |
| DOI: | 10.1109/83.661182 |