R. Acar and C. R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems, Inverse Problems, vol.10, issue.6, pp.1217-1229, 1994.
DOI : 10.1088/0266-5611/10/6/003

L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford mathematical monographs, 2000.

H. Attouch, L. M. Briceño-arias, and P. L. Combettes, A Parallel Splitting Method for Coupled Monotone Inclusions, SIAM Journal on Control and Optimization, vol.48, issue.5, p.3246, 2010.
DOI : 10.1137/090754297

H. Attouch, . Buttazzo, and G. Michaille, Variational analysis in Sobolev and BV spaces : applications to PDEs and optimization. MPS-SIAM series on optimization, 2006.
DOI : 10.1137/1.9781611973488

G. Aubert and J. F. Aujol, Modeling Very Oscillating Signals. Application to Image Processing, Applied Mathematics and Optimization, vol.51, issue.2, pp.163-182, 2005.
DOI : 10.1007/s00245-004-0812-z
URL : https://hal.archives-ouvertes.fr/hal-00202000

G. Aubert, J. F. Aujol, L. Blanc-feraud, and A. Chambolle, Image decomposition into a bounded variation component and an oscillating component, Journal of Mathematical Imaging and Vision, vol.22, issue.1, pp.71-88, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00202001

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing, Partial Differential Equations and the Calculus of Variations, Applied Mathematical Sciences, vol.147, 2006.

J. F. Aujol, Some First-Order Algorithms for Total Variation Based Image Restoration, Journal of Mathematical Imaging and Vision, vol.33, issue.2, pp.307-327, 2009.
DOI : 10.1007/s10851-009-0149-y
URL : https://hal.archives-ouvertes.fr/hal-00260494

A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, vol.20, pp.89-97, 2004.

F. Demengel, FonctionsàFonctionsà hessien borné Annales de l'institut Fourier, pp.155-190, 1984.
DOI : 10.5802/aif.969
URL : http://archive.numdam.org/article/AIF_1984__34_2_155_0.pdf

R. Echegut and L. Piffet, A Variational Model for Image Texture Identification
DOI : 10.1007/978-3-642-12598-0_41
URL : https://hal.archives-ouvertes.fr/hal-00439431

I. Ekeland and R. Temam, Convex Analysis and Variational problems, SIAM Classic in Applied Mathematics, vol.28, 1999.
DOI : 10.1137/1.9781611971088

J. Fadili and G. Peyré, Total Variation Projection with First Order Schemes, Preprint

J. B. Garnett, . Le, M. Triet, Y. Meyer, and L. A. Vese, Image decompositions using bounded variation and generalized homogeneous Besov spaces, Applied and Computational Harmonic Analysis, vol.23, issue.1, pp.25-56, 2007.
DOI : 10.1016/j.acha.2007.01.005

W. Hinterberger and O. Scherzer, Variational Methods on the Space of Functions of Bounded Hessian for Convexification and Denoising, Computing, vol.80, issue.3, pp.109-133, 2006.
DOI : 10.1007/s00607-005-0119-1

B. Hofmann, B. Kaltenbacher, C. Pöschl, and O. Scherzer, A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators, Inverse Problems, vol.23, issue.3, pp.987-1010, 2007.
DOI : 10.1088/0266-5611/23/3/009

T. M. Le and L. A. Vese, ), Multiscale Modeling & Simulation, vol.4, issue.2
DOI : 10.1137/040610052

L. H. Lieu and L. A. Vese, Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces, Applied Mathematics and Optimization, vol.19, issue.1???3, pp.167-193, 2008.
DOI : 10.1007/s00245-008-9047-8

Y. Meyer, Oscillating patterns in image processing and nonlinear evolution equations, 2002.
DOI : 10.1090/ulect/022

S. Osher, E. Fatemi, and L. Rudin, Nonlinear total variation based noise removal algorithms, Physica D, vol.60, pp.259-268, 1992.

S. Osher, A. Sole, and L. Vese, Image decomposition and restoration using total variation minimization and the H 1 norm, SIAM Journal on Multiscale Modeling and Simulation, pp.1-3, 2003.

S. Osher and L. Vese, Modeling textures with total variation minimization and oscillating patterns in image processing, Journal of Scientific Computing, vol.19, pp.1-3, 2003.

S. J. Osher and L. A. Vese, Image denoising and decomposition with total variation minimization and oscillatory functions. Special issue on mathematics and image analysis, J. Math. Imaging Vision, vol.20, issue.12, pp.7-18, 2004.

L. Piffet, Modèles variationnels pour l'extraction de textures 2D, 2010.

P. Weiss, L. Blanc-féraud, and G. Aubert, Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing, SIAM Journal on Scientific Computing, vol.31, issue.3, 2009.
DOI : 10.1137/070696143
URL : https://hal.archives-ouvertes.fr/inria-00166096

W. Yin, D. Goldfarb, and S. Osher, A comparison of three total variation based texture extraction models, Journal of Visual Communication and Image Representation, vol.18, issue.3, pp.240-252, 2007.
DOI : 10.1016/j.jvcir.2007.01.004