期刊
SIAM JOURNAL ON IMAGING SCIENCES
卷 7, 期 4, 页码 2393-2422出版社
SIAM PUBLICATIONS
DOI: 10.1137/140954039
关键词
denoising; total variation; scale-space; generalized Laplacian; Riemannian manifold; vector bundle
类别
资金
- European Research Council Starting Grant [306337]
- European Research Council (ERC) [306337] Funding Source: European Research Council (ERC)
We present a generalization of the Euclidean and Riemannian gradient operators to a vector bundle, a geometric structure generalizing the concept of a manifold. One of the key ideas is to replace the standard differentiation of a function by the covariant differentiation of a section. Dealing with covariant derivatives satisfying the property of compatibility with vector bundle metrics, we construct generalizations of existing mathematical models for image regularization that involve the Euclidean gradient operator, namely, the linear scale-space and the Rudin-Osher-Fatemi denoising models. For well-chosen covariant derivatives, we show that our denoising model outperforms state-of-the-art variational denoising methods of the same type both in terms of peak signal-to-noise ratio (PSNR) and Q-index [Z. Wang and A. Bovik, IEEE Signal Process. Lett., 9 (2002), pp. 81-84].
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