A class of nonlinear parabolic-hyperbolic equations applied to image restoration

Nonlinear Analysis: Real World Applications

Volumn 11, Issue 1, 2010, Pages 253-261

  Cao, Yang ^a   Yin, Jingxue ^a   Liu, Qiang ^a   Li, Meihui ^a  

^a JILIN UNIVERSITY   (China)

Author keywords

Image restoration; Parabolic hyperbolic equation; Well posedness

Indexed keywords

EXPERIMENTAL APPROACHES; HYPERBOLIC EQUATIONS; IMAGE RESTORATION; PARABOLIC-HYPERBOLIC EQUATION; WELL-POSEDNESS;

IMAGE RECONSTRUCTION; PARTIAL DIFFERENTIAL EQUATIONS; RESTORATION;

NONLINEAR EQUATIONS;

EID: 70350734095     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.11.004     Document Type: Article

References (22)

1. Alvarez L., and Mazorra L. Signal and image restoration using shock filters and anisotropic diffusion. SIAM J. Numer. Anal. 31 2 (1994) 590-605
2. Perona P., and Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell. 12 7 (1990) 629-639
3. Chan T.F., Golub G.H., and Mulet P. A nonlinear primal-dual method for total variation-based image restoration. SIAM J. Sci. Comput. 20 6 (1999) 1964-1977
4. Rudin L.I., Osher S., and Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259-268
5. Vogel C.R., and Oman M.E. Iterative methods for total variation denoising. SIAM J. Sci. Comput. 17 1 (1996) 227-238
6. Chan T.F., Marquina A., and Mulet P. High-order total variation-based image restoration. SIAM J. Sci. Comput. 22 2 (2000) 503-516
7. Lysaker M., Lundervold A., and Tai X.C. Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Tran. Image Process. 12 12 (2003) 1579-1590
8. Qiang Q., Yao Z.A., and Ke Y.Y. Entropy solutions for a fourth-order nonlinear degenerate problem for noise removal. Nonlinear Anal. TMA 2007 67 (2007) 1908-1918
9. Gilboa G., Sochen N., and Zeevi Y.Y. Image enhancement and denoising by complex diffusion process. IEEE Trans. Pattern Anal. Machine Intell. 26 8 (2004) 1020-1036
10. V. Ratner, Y.Y. Zeevi, Image enhancement using elastic manifolds, ICIAP 2007, 14th International Conference on Image Analysis and Processing, 2007, pp. 769-774
11. Park J.Y., and Jeong J.U. Optimal Control of dampt Klein-Gordon equations with state constraints. J. Math. Anal. Appl. 334 (2007) 11-27
12. Averbuch A., Epstein B., Rabin N., and Turkel E. Edge-enhancement postprocessing using artificial dissipation. IEEE Trans. Image Process. 15 6 (2006) 1486-1498
13. Aubert G., and Kornprobst P. Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Applied Mathematical Sciences vol. 147 (2002), Springer-Verlag
14. Evans L.C. Partial Differential Equations. Graduate Studies in Mathematics vol. 19 (1998), American Mathematical Society, Providence, Rhode Island
15. Lions J.L. Quelques méthodes de résolution des problèmes aux limites non linéaires (1969), Dunod, Gauthier-Villars, Paris
16. Gao P., and Guo B. The time-periodic solution for a 2D dissipative Klein-Gordon equation. J. Math. Anal. Appl. 296 2 (2004) 686-694
17. Kapitanski L. Global and unique weak solutions of nonlinear wave equations. Math. Res. Lett. 1 2 (1994) 211-223
18. Lin Y., and Cui M. A new method to solve the damped nonlinear Klein-Gordon equation. Sci. China Ser. A 51 2 (2008) 304-313
19. Nakagiri S.-i., and Ha J.-h. Optimal Control Problems for Damped Klein-Gordon Equations. Nonlinear Anal. 47 1 (2001) 89-100
20. Khalifa M.E., and Elgamal M. A numerical solution to Klein-Gordon equation with Dirichlet boundary condition. Appl. Math. Comput. 160 2 (2005) 451-475
21. Adams R. Sobolev spaces. Pure and Applied Mathematics Series of Monographs and Textbooks vol. 65 (1975), Academic Press, Inc., New York, SanFrancisco, London
22. Catté F., Lions P.L., Morel J.M., and Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29 1 (1992) 182-193