Litt´ erature
1. Acar, R., Vogel, C. : Analysis of bounded variation penalty methods for ill-posed
problems. Inverse Problems 10(6), 1217–1229 (1994)
2. Adams, R. : Sobolev spaces. Academic Press, Springer Verlag (1978)
3. Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M. : Axioms and fundamental equations
of image processing. Arch. Rational Mechanics and Anal. 16(9), 200–257 (1993)
4. Ambrosio, L., Fusco, N., Pallara, D. : Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press Oxford
University Press, New York (2000)
5. Ambrosio, L., Tortorelli, V. : Approximation of functionnals depending on jumps by
elliptic functionnals via gammaconvergence. Communications on Pure and Applied
Mathematics XLIII, 999–1036 (1990)
6. Attouch, H., Buttazzo, G., Michaille, G. : Variational analysis in Sobolev and BV
spaces, MPS/SIAM Series on Optimization, vol. 6. Society for Industrial and Applied
Mathematics (SIAM), Philadelphia, PA (2006). Applications to PDEs and optimization
7. Aubert, G., Barlaud, M., Faugeras, O., Jehan-Besson, S. : Image segmentation using
active contours : calculus of variations or shape gradients ? SIAM J. Appl. Math.
63(6), 2128–2154 (2003)
8. Aubert, G., Kornprobst, P. : Mathematical Problems in Image Processing, Partial
Differential Equations and the Calculus of Variations., Applied Mathematical Sciences,
vol. 147. Springer (2006)
9. Aubert, G., Vese, L. : A variational method in image recovery. SIAM J. Numer. Anal.
34(5), 1948–1979 (1997)
10. Aujol, J.F. : Traitement d’images par approches variationnelles et ´ equations aux
d´ eriv´ ees partielles. Cours de DEA. 11-16 avril 2005 , ENIT Tunis (2005). URL
http://cel.archives-ouvertes.fr/cel-00148665
11. Aujol, J.F. : Some first-order algorithms for total variation based image restoration.
J. Math. Imaging Vision 34(3), 307–327 (2009)
12. Aujol, J.F., Aubert, G., Blanc-F´ eraud, L., Chambolle, A. : Image decomposition into a
bounded variation component and an oscillating component. J. Math. Imaging Vision
22(1), 71–88 (2005)
13. Az´ e, D. : ´
El´ ements d’analyse convexe et variationnelle. Ellipses (1997)
14. Barbu, V., Precupanu, T. : Convexity and Optimization in Banach Spaces. Sijthoff &
Noordhoff, Bucarest (1978)
Ó Springer-Verlag Berlin Heidelberg 2015
M. Bergounioux, Introduction au traitement mathématique des
images - méthodes déterministes, Mathématiques et Applications 76,
DOI 10.1007/978-3-662-46539-4
233
1. Acar, R., Vogel, C. : Analysis of bounded variation penalty methods for ill-posed
problems. Inverse Problems 10(6), 1217–1229 (1994)
2. Adams, R. : Sobolev spaces. Academic Press, Springer Verlag (1978)
3. Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M. : Axioms and fundamental equations
of image processing. Arch. Rational Mechanics and Anal. 16(9), 200–257 (1993)
4. Ambrosio, L., Fusco, N., Pallara, D. : Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press Oxford
University Press, New York (2000)
5. Ambrosio, L., Tortorelli, V. : Approximation of functionnals depending on jumps by
elliptic functionnals via gammaconvergence. Communications on Pure and Applied
Mathematics XLIII, 999–1036 (1990)
6. Attouch, H., Buttazzo, G., Michaille, G. : Variational analysis in Sobolev and BV
spaces, MPS/SIAM Series on Optimization, vol. 6. Society for Industrial and Applied
Mathematics (SIAM), Philadelphia, PA (2006). Applications to PDEs and optimization
7. Aubert, G., Barlaud, M., Faugeras, O., Jehan-Besson, S. : Image segmentation using
active contours : calculus of variations or shape gradients ? SIAM J. Appl. Math.
63(6), 2128–2154 (2003)
8. Aubert, G., Kornprobst, P. : Mathematical Problems in Image Processing, Partial
Differential Equations and the Calculus of Variations., Applied Mathematical Sciences,
vol. 147. Springer (2006)
9. Aubert, G., Vese, L. : A variational method in image recovery. SIAM J. Numer. Anal.
34(5), 1948–1979 (1997)
10. Aujol, J.F. : Traitement d’images par approches variationnelles et ´ equations aux
d´ eriv´ ees partielles. Cours de DEA. 11-16 avril 2005 , ENIT Tunis (2005). URL
http://cel.archives-ouvertes.fr/cel-00148665
11. Aujol, J.F. : Some first-order algorithms for total variation based image restoration.
J. Math. Imaging Vision 34(3), 307–327 (2009)
12. Aujol, J.F., Aubert, G., Blanc-F´ eraud, L., Chambolle, A. : Image decomposition into a
bounded variation component and an oscillating component. J. Math. Imaging Vision
22(1), 71–88 (2005)
13. Az´ e, D. : ´
El´ ements d’analyse convexe et variationnelle. Ellipses (1997)
14. Barbu, V., Precupanu, T. : Convexity and Optimization in Banach Spaces. Sijthoff &
Noordhoff, Bucarest (1978)
Ó Springer-Verlag Berlin Heidelberg 2015
M. Bergounioux, Introduction au traitement mathématique des
images - méthodes déterministes, Mathématiques et Applications 76,
DOI 10.1007/978-3-662-46539-4
233