Abstract
In this paper, we propose a new model for image restoration and image decomposition into cartoon and texture, based on the total variation minimization of Rudin, Osher, and Fatemi [Phys. D, 60 (1992), pp. 259--268], and on oscillatory functions, which follows results of Meyer [Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, Univ. Lecture Ser. 22, AMS, Providence, RI, 2002]. This paper also continues the ideas introduced by the authors in a previous work on image decomposition models into cartoon and texture [L. Vese and S. Osher, J. Sci. Comput., to appear]. Indeed, by an alternative formulation, an initial image f is decomposed here into a cartoon part u and a texture or noise part v. The u component is modeled by a function of bounded variation, while the v component is modeled by an oscillatory function, bounded in the norm dual to $|\cdot|_{H^1_0}$. After some transformation, the resulting PDE is of fourth order, envolving the Laplacian of the curvature of level lines. Finally, image decomposition, denoising, and deblurring numerical results are shown.
Keywords
DeblurringBounded variationMathematicsImage restorationBounded functionNorm (philosophy)Laplace operatorApplied mathematicsTotal variation denoisingImage (mathematics)Image processingAlgorithmMathematical analysisArtificial intelligenceComputer science
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Publication Info
- Year
- 2003
- Type
- article
- Volume
- 1
- Issue
- 3
- Pages
- 349-370
- Citations
- 587
- Access
- Closed
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Cite This
Stanley Osher,
Andrés Solé,
Luminita A. Vese
(2003).
Image Decomposition and Restoration Using Total Variation Minimization and the<i>H</i><sup>1</sup>.
Multiscale Modeling and Simulation
, 1
(3)
, 349-370.
https://doi.org/10.1137/s1540345902416247
Identifiers
- DOI
- 10.1137/s1540345902416247