L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

G. Evangelopoulos and P. Maragos, Image decomposition into structure and texture subcomponents with multifrequency modulation constraints, 2008 IEEE Conference on Computer Vision and Pattern Recognition, pp.23-28, 2008.
DOI : 10.1109/CVPR.2008.4587649

J. Aujol and T. F. Chan, Combining geometrical and textured information to perform image classification, Journal of Visual Communication and Image Representation, vol.17, issue.5, pp.1004-1023, 2006.
DOI : 10.1016/j.jvcir.2006.02.001
URL : https://hal.archives-ouvertes.fr/hal-00201972

J. Frecon, N. Pustelnik, H. Wendt, L. Condat, and P. Abry, Multifractalbased texture segmentation using variational procedure, Proc. of the 12th Image, Video, and Multidimensional Signal Processing Workshop, pp.11-12, 2016.
DOI : 10.1109/ivmspw.2016.7528187
URL : https://hal.archives-ouvertes.fr/hal-01398865

M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, Simultaneous structure and texture image inpainting, IEEE Transactions on Image Processing, vol.12, issue.8, pp.882-889, 2003.
DOI : 10.1109/TIP.2003.815261
URL : http://www.math.ucla.edu/~lvese/PAPERS/01211536.pdf

S. Osher, A. Solé, and L. Vese, Multiscale Modeling & Simulation, vol.1, issue.3, pp.349-370, 2003.
DOI : 10.1137/S1540345902416247

J. Aujol, G. Gilboa, T. Chan, and S. Osher, Structure-Texture Image Decomposition???Modeling, Algorithms, and Parameter Selection, International Journal of Computer Vision, vol.4, issue.2, pp.111-136, 2006.
DOI : 10.1023/B:JMIV.0000011320.81911.38
URL : https://hal.archives-ouvertes.fr/hal-00201977

L. M. Briceño-arias, P. L. Combettes, J. Pesquet, and N. Pustelnik, Proximal method for geometry and texture image decomposition, 2010 IEEE International Conference on Image Processing, pp.26-29, 2010.
DOI : 10.1109/ICIP.2010.5653670

L. M. Briceño-arias, P. L. Combettes, J. Pesquet, and N. Pustelnik, Proximal Algorithms for Multicomponent Image Recovery Problems, Journal of Mathematical Imaging and Vision, vol.30, issue.1-2, pp.3-22, 2011.
DOI : 10.1142/9789812777096

N. Pustelnik, H. Wendt, and P. Abry, Local regularity for texture segmentation: Combining wavelet leaders and proximal minimization, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.26-31, 2013.
DOI : 10.1109/ICASSP.2013.6638684
URL : https://hal.archives-ouvertes.fr/hal-00826839

R. M. Haralick, Statistical and structural approaches to texture, Proc. of the IEEE, pp.786-804, 1979.
DOI : 10.1109/PROC.1979.11328

D. Blostein and N. Ahuja, A multiscale region detector, Computer Vision, Graphics, and Image Processing, vol.45, issue.1, pp.22-41, 1989.
DOI : 10.1016/0734-189X(89)90068-6
URL : http://vision.ai.uiuc.edu/publications/multiscale_region_detector_CVGIP_1989.pdf

T. Lindeberg, Feature detection with automatic scale selection, International Journal of Computer Vision, vol.30, issue.2, pp.79-116, 1998.
DOI : 10.1023/A:1008045108935

C. A. Kak and M. Slaney, Principles of computerized tomographic imaging, 1988.
DOI : 10.1118/1.1455742
URL : https://aapm.onlinelibrary.wiley.com/doi/pdf/10.1118/1.1455742

E. Chouzenoux, F. Zolyniak, E. Gouillart, and H. Talbot, A majorizeminimize memory gradient algorithm applied to X-ray tomography, Proc. of the 20th International Conference on Image Processing, pp.1011-1015, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00830052

R. A. Ketcham and W. D. Carlson, Acquisition, optimization and interpretation of X-ray computed tomographic imagery: applications to the geosciences, Computers & Geosciences, vol.27, issue.4, pp.381-400, 2001.
DOI : 10.1016/S0098-3004(00)00116-3

E. Gouillart, F. Krzakala, M. Mezard, and L. Zdeborová, Belief-propagation reconstruction for discrete tomography, Inverse Problems, vol.29, issue.3, p.35003, 2013.
DOI : 10.1088/0266-5611/29/3/035003
URL : https://hal.archives-ouvertes.fr/hal-00750511

M. H. Wright, Interior methods for constrained optimization, Acta Numerica, vol.26, pp.341-407, 1991.
DOI : 10.1007/BF02592025

J. Gondzio, Interior point methods 25 years later, European Journal of Operational Research, vol.218, issue.3, pp.587-601, 2012.
DOI : 10.1016/j.ejor.2011.09.017
URL : http://www.maths.ed.ac.uk/~gondzio/reports/ipmXXV.pdf

A. Forsgren, P. E. Gill, and M. H. Wright, Interior Methods for Nonlinear Optimization, SIAM Review, vol.44, issue.4, pp.525-597, 2002.
DOI : 10.1137/S0036144502414942

P. Armand, J. C. Gilbert, and S. Jan-jégou, A Feasible BFGS Interior Point Algorithm for Solving Convex Minimization Problems, SIAM Journal on Optimization, vol.11, issue.1, pp.199-222, 2000.
DOI : 10.1137/S1052623498344720
URL : https://hal.archives-ouvertes.fr/inria-00073185

S. Bonettini and T. Serafini, Non-negatively constrained image deblurring with an inexact interior point method, Journal of Computational and Applied Mathematics, vol.231, issue.1, pp.236-248, 2009.
DOI : 10.1016/j.cam.2009.02.020
URL : https://doi.org/10.1016/j.cam.2009.02.020

H. H. Bauschke, P. L. Combettes-corbineau, E. Chouzenoux, and J. Pesquet, Convex analysis and monotone operator theory in Hilbert spaces PIPA: a new proximal interior point algorithm for large-scale convex optimization, Proc. of the 43rd International Conference on Acoustics, Speech and Signal Processing, pp.15-20, 2011.
DOI : 10.1007/978-3-319-48311-5

P. L. Combettes and V. R. Wajs, Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005.
DOI : 10.1137/050626090
URL : https://hal.archives-ouvertes.fr/hal-00017649

P. L. Combettes and J. Pesquet, Proximal splitting methods in signal processing, " in Fixed-point algorithms for inverse problems in science and engineering, pp.185-212, 2011.

E. Chouzenoux, S. Moussaoui, and J. Idier, Majorize???minimize linesearch for inversion methods involving barrier function optimization, Inverse Problems, vol.28, issue.6, p.65011, 2012.
DOI : 10.1088/0266-5611/28/6/065011
URL : https://hal.archives-ouvertes.fr/hal-00697876

S. Salzo, The Variable Metric Forward-Backward Splitting Algorithm Under Mild Differentiability Assumptions, SIAM Journal on Optimization, vol.27, issue.4, pp.2153-2181, 2017.
DOI : 10.1137/16M1073741
URL : http://arxiv.org/pdf/1605.00952

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

S. Becker and J. Fadili, A quasi-newton proximal splitting method, Proc. of the 25th Advances in Neural Information Processing Systems Conference (NIPS 2012), pp.3-8, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00710900

E. Chouzenoux, J. Pesquet, and A. Repetti, Variable Metric Forward???Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function, Journal of Optimization Theory and Applications, vol.21, issue.2, pp.107-132, 2014.
DOI : 10.1118/1.597290
URL : https://hal.archives-ouvertes.fr/hal-00789970

S. Setzer, G. Steidl, and T. Teuber, Deblurring Poissonian images by split Bregman techniques, Journal of Visual Communication and Image Representation, vol.21, issue.3, pp.193-199, 2010.
DOI : 10.1016/j.jvcir.2009.10.006
URL : http://www.mathematik.uni-kl.de/uploads/tx_sibibtex/poisson_deblurring_elsevier_revised2.pdf

A. A. Proussevitch, D. L. Sahagian, and W. D. Carlson, Statistical analysis of bubble and crystal size distributions: Application to Colorado Plateau basalts, Journal of Volcanology and Geothermal Research, vol.164, issue.3, pp.112-126, 2007.
DOI : 10.1016/j.jvolgeores.2007.04.006