Image decomposition & restoration using total variation minimization & the H-1 norm

Multiscale Modeling and Simulation

Volumn 1, Issue 3, 2003, Pages 349-370

  Osher, Stanley ^a   Solé, Andrés ^b   Vese, Luminita ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Cartoon; Functional minimization; Image decomposition; Partial differential equation; Restoration; Texture; Total variation

Indexed keywords

IMAGE DENOISING; IMAGE ENHANCEMENT; IMAGE PROCESSING; IMAGE RECONSTRUCTION; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RESTORATION; TEXTURES;

CARTOON; FUNCTIONAL MINIMIZATION; IMAGE DECOMPOSITION; IMAGE DECOMPOSITION MODELS; NONLINEAR EVOLUTION EQUATION; OSCILLATORY FUNCTIONS; TOTAL VARIATION; TOTAL VARIATION MINIMIZATION;

IMAGE TEXTURE;

EID: 33749252638     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/S1540345902416247     Document Type: Article

References (24)

1. R. Acart and C.R. Vogel, Analysis of bounded variation penalty methods of ill-posed problems, Inverse Problems, 10 (1994), pp. 1217-1229.
2. F. Andreu, C. Ballester, V. Caselles, and J.M. Mazon, Minimizing total variation flow, C. R. Acad. Sci. Paris Śer. I Math., 331 (2000), pp. 867-872.
3. J.-F. Aujol, G. Aubert, L. Blanc-Féraud, and A. Chambolle, Image Decomposition: Application to Textured Images and SAR Images, Rapport de Recherche RR 4704, INRIA, Sophia-Antipolis Cedex, France, 2003.
4. M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, Simultaneous structure and texture image inpainting, IEEE Trans. Image Process., to appear.
5. S. Casadei, S. Mitter, and P. Perona, Boundary detection in piecewise homogeneous textured images, in Computer Vision-ECCV '92, Lecture Notes in Comput. Sci. 588, Springer-Verlag, Berlin, 1992, pp. 174-183.
6. A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vision, to appear.
7. A. Chambolle and P.L. Lions, Image recovery via total variation minimization and related problems, Numer. Math., 76 (1997), pp. 167-188.
8. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 2, Functional and Variational Methods, Springer-Verlag, Berlin, 1988.
9. Y. Ekeland and R. Temam, Analyse Convexe et Problèmes Variationnels, Dunod, Gauthier- Villars, Paris, 1974.
10. L.C. Evans, Partial Differential Equations, Grad. Stud. Math. 19, AMS, Providence, RI, 1998.
11. J.B. Greer and A.L. Bertozzi, H1 Solutions of a Class of Fourth Order Nonlinear Equations for Image Processing, UCLA CAM Report 03-11, UCLA, Los Angeles, CA, 2003.
12. M. Lysaker, A. Lundervold, and X.-C. Tai, Noise Removal Using Fourth-Order Partial Differential Equations with Applications to Medical Magnetic Resonance Images in Space and Time, UCLA CAM Report 02-44, UCLA, Los Angeles, CA, 2002.
13. F. Malgouyres, Mathematical analysis of a model which combines total variation and wavelet for image restoration, J. Information Processes, 2 (2002), pp. 1-10.
14. F. Malgouyres, Minimizing the total variation under a general convex constraint for image restoration, IEEE Trans. Image Process., 11 (2002), pp. 1450-1456.
15. Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, Univ. Lecture Ser. 22, AMS, Providence, RI, 2002.
16. D. Mumford and B. Gidas, Stochastic models for generic images, Quart. Appl. Math., 59 (2001), pp. 85-111.
17. F. Oru, Le rôle des oscillations dans quelques problèmes d'analyse non-lińeaire, Thèse, CMLA, ENS-Cachan, Cachan cedex, France, 1998.
18. L. Rudin and S. Osher, Total variation based image restoration with free local constraints, in Proceedings of the IEEE ICIP 1994, Vol. I, Austin, TX, pp. 31-35.
19. L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
20. L. Vese, A study in the BV space of a denoising-deblurring variational problem, Appl. Math. Optim., 44 (2001), pp. 131-161.
21. L. Vese and S. Osher, Modeling textures with total variation minimization and oscillating patterns in image processing, J. Sci. Comput., to appear.
22. L. Vese and S. Osher, Image denoising and decomposition with total variation minimization and oscillatory functions, J. Math. Imaging Vision, to appear.
23. S.C. Zhu, Y.N. Wu, and D. Mumford, Filters, random fields and maximum entropy (FRAME): Towards a unified theory for texture modeling, Internat. J. Computer Vision, 27 (1998), pp. 107-126.
24. S.C. Zhu, Y.N. Wu, and D. Mumford, Minimax entropy principle and its application to texture modeling, Neural Computation, 9 (1997), pp. 1627-1660.