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High-Order Total Variation-Based Image Restoration
Abstract
The total variation (TV) denoising method is a PDE-based technique that preserves edges well but has the sometimes undesirable staircase effect, namely, the transformation of smooth regions ( ramps) into piecewise constant regions ( stairs). In this paper we present an improved model, constructed by adding a nonlinear fourth order diffusive term to the Euler--Lagrange equations of the variational TV model. Our technique substantially reduces the staircase effect, while preserving sharp jump discontinuities (edges). We show numerical evidence of the power of resolution of this novel model with respect to the TV model in some 1D and 2D numerical examples.
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Cited by
An Iterative Regularization Method for Total Variation-Based Image Restoration
Osher, S., Burger, M., Goldfarb, D., Xu, J., & Yin, W. (2005) · Multiscale Modeling & Simulation · doi:10.1137/040605412 · Cited by 1,787
Bredies, K., Kunisch, K., & Pock, T. (2010) · SIAM Journal on Imaging Sciences · doi:10.1137/090769521 · Cited by 1,535
Lysaker, M., Lundervold, A., & Tai, X.-C. (2003) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.819229 · Cited by 911
Wu, C., & Tai, X.-C. (2010) · SIAM Journal on Imaging Sciences · doi:10.1137/090767558 · Cited by 615
Metadata
- Authors
- Chan, T., Marquina, A., & Mulet, P.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2000-01
- Volume
- 22
- Issue
- 2
- Pages
- 503-516
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2037981501
- Cited by
- 776
- References
- 0
- FWCI
- 6.58
- Type
- journal article
- Language
- en
- Open access
- closed
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- Chan, T., Marquina, A., & Mulet, P. (2000). High-Order Total Variation-Based Image Restoration. SIAM Journal on Scientific Computing. https://doi.org/10.1137/s1064827598344169
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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