Open Access
Issue |
ESAIM: COCV
Volume 31, 2025
|
|
---|---|---|
Article Number | 62 | |
Number of page(s) | 44 | |
DOI | https://doi.org/10.1051/cocv/2025048 | |
Published online | 18 July 2025 |
- M. Bertalmio, G. Sapiro, V. Caselles and C. Ballester, Image inpainting, Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (USA), SIGGRAPH '00. ACM Press/Addison-Wesley Publishing Co. (2000) 417-424. [Google Scholar]
- J. Shen and T.F. Chan, Mathematical models for local nontexture inpaintings. SIAM J. Appl. Math. 62 (2002) 1019-1043. [Google Scholar]
- C.-B. Schönlieb, Partial Differential Equation Methods for Image Inpainting, vol. 29. Cambridge University Press (2015). [Google Scholar]
- A. Bertozzi, S. Esedoglu and A. Gillette, Inpainting of binary images using the Cahn-Hilliard equation. IEEE Trans.Image Process. 16 (2006) 285-291. [Google Scholar]
- A. Bertozzi, S. Esedoglu and A. Gillette, Analysis of a two-scale Cahn-Hilliard model for binary image inpainting. Multiscale Model. Simul. 6 (2007) 913-936. [Google Scholar]
- T.F. Chan and J. Shen, Image processing and analysis. Variational, PDE, wavelet, and stochastic methods. Society for Industrial and Applied Mathematics (2005). [Google Scholar]
- C. Guillemot and O. Le Meur, Image inpainting: overview and recent advances. IEEE signal Process. Mag. 31 (2013) 127-144. [Google Scholar]
- O. Scherzer, Handbook of Mathematical Methods in Imaging. Springer Science & Business Media (2010). [Google Scholar]
- A. Criminisi, P. Perez and K. Toyama, Region filling and object removal by exemplar-based image inpainting. IEEETrans. Image Process. 13 (2004) 1200-1212. [Google Scholar]
- O. Elharrouss, N. Almaadeed, S. Al-Maadeed and Y. Akbari, Image inpainting: a review. Neural Process. Lett. 51 (2020) 2007-2028. [Google Scholar]
- J. Bosch, D. Kay, M. Stoll and A.J. Wathen, Fast solvers for Cahn-Hilliard inpainting. SIAM J. Imaging Sci. 7 (2014) 67-97. [Google Scholar]
- J. Bosch and M. Stoll, A fractional inpainting model based on the vector-valued Cahn-Hilliard equation. SIAM J.Imaging Sci. 8 (2015) 2352-2382. [Google Scholar]
- M. Burger, L. He and C.-B. Schönlieb, Cahn-Hilliard inpainting and a generalization for grayvalue images. SIAMJ. Imaging Sci. 2 (2009) 1129-1167. [Google Scholar]
- L. Cherfils, H. Fakih and A. Miranville, A Cahn-Hilliard system with a fidelity term for color image inpainting. J.Math. Imaging Vision 54 (2016) 117-131. [Google Scholar]
- L. Cherfils, H. Fakih and A. Miranville, A complex version of the Cahn-Hilliard equation for grayscale image inpainting. Multiscale Model. Simul. 15 (2017) 575-605. [Google Scholar]
- H. Garcke, K.F. Lam and V. Styles, Cahn-Hilliard inpainting with the double obstacle potential. SIAM J. ImagingSci. 11 (2018) 2064-2089. [Google Scholar]
- A. Novak and N. Reinic, Shock filter as the classifier for image inpainting problem using the Cahn-Hilliard equation. Comput. Math. Appl. 123 (2022) 105-114. [Google Scholar]
- A. Theljani, H. Houichet and A. Mohamed, An adaptive Cahn-Hilliard equation for enhanced edges in binary image inpainting. J. Algorithms Comput. Technol. 14 (2020) 10. [Google Scholar]
- L. Modica and S. Mortola, Un esempio di T-convergenza. Boll. Un. Mat. Ital. B 14 (1977) 285-299. [MathSciNet] [Google Scholar]
- S. Esedoglu and J. Shen, Digital inpainting based on the Mumford-Shah-Euler image model. European J. Appl.Math. 13 (2002) 353-370. [Google Scholar]
- L. Cherfils, H. Fakih and A. Miranville, On the Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation with logarithmic nonlinear terms. SIAM J. Imaging Sci. 8 (2015) 1123-1140. [Google Scholar]
- K.F. Lam, Global and exponential attractors for a Cahn-Hilliard equation with logarithmic potentials and mass source. J. Differ. Equ. 312 (2022) 237-275. [CrossRef] [Google Scholar]
- A. Miranville, The Cahn-Hilliard equation with a nonlinear source term. J. Differ. Equ. 294 (2021) 88-117. [CrossRef] [Google Scholar]
- P. Colli, G. Gilardi, E. Rocca and J. Sprekels, Well-posedness and optimal control for a Cahn-Hilliard-Oono system with control in the mass term. Discrete Contin. Dyn. Syst.-S 15 (2022) 2135-2172. [Google Scholar]
- C.G. Gal and A. Poiatti, Unified framework for the separation property in binary phase-segregation processes with singular entropy densities, European J. Appl. Math. 36 (2025) 40-67. [Google Scholar]
- M. Grasselli and A. Poiatti, The Cahn-Hilliard-Boussinesq system with singular potential. Commun. Math. Sci. 20 (2022) 897-946. [Google Scholar]
- J. Simon, Compact sets in the space Lp(0,T; B). Ann. Mat. Pura Appl. 146 (1986) 65-96. [CrossRef] [Google Scholar]
- E. Casas, J.C. de los Reyes and F. Tröltzsch, Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints. SIAM J. Optim. 19 (2008) 616-643. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas and F. Troöltzsch, Second order analysis for optimal control problems: improving results expected from abstract theory. SIAM J. Optim. 22 (2012) 261-279. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas, F. Troltzsch and A. Unger, Second order sufficient optimality conditions for some state-constrained control problems of semilinear elliptic equations. SIAM J. Control Optim. 38 (2000) 1369-1391. [Google Scholar]
- F. Troltzsch, Optimal control of partial differential equations: theory, methods and applications. Graduate Studies in Mathematics, vol. 112. American Mathematical Society, Providence, RI (2010). [Google Scholar]
- M. Abatangelo, C. Cavaterra, M. Grasselli and H. Wu, Optimal distributed control for a Cahn-Hilliard-Darcy system with mass sources, unmatched viscosities and singular potential. ESAIM Control Optim. Calc. Var. 30 (2024) Paper No. 52, 49. [Google Scholar]
- P. Colli, M.H. Farshbaf-Shaker, G. Gilardi and J. Sprekels, Second-order analysis of a boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions. Ann. Acad. Rom. Sci. Ser. Math. Appl. 7 (2015) 41-66. [Google Scholar]
- P. Colli, A. Signori and J. Sprekels, Second-order analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis. ESAIM Control Optim. Calc. Var. 27 (2021) 73. [Google Scholar]
- P. Colli and J. Sprekels, Second-order optimality conditions for the sparse optimal control of nonviscous Cahn- Hilliard systems. arXiv preprint arXiv:2406.02384 (2024). [Google Scholar]
- M. Ebenbeck and P. Knopf, Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth. ESAIM Control Optim. Calc. Var. 26 (2020) Paper No. 71, 38. [Google Scholar]
- J. Sprekels and F. Troltzsch, Second-order sufficient conditions in the sparse optimal control of a phase field tumor growth model with logarithmic potential. ESAIM: Control Optim. Calc. Var. 30 (2024) 13. [Google Scholar]
- E. Casas and F. Troltzsch, Second order optimality conditions and their role in PDE control. Jahresber. Dtsch.Math.-Ver. 117 (2015) 3-44. [Google Scholar]
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