A new proximal method for joint image restoration and edge detection with the Mumford-Shah model, Proc. Int. Conf. Acoust., Speech Signal Process, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01736997
Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography, Journal of Theoretical Biology, vol.29, issue.3, pp.471-481, 1970. ,
DOI : 10.1016/0022-5193(70)90109-8
Richardson???Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution, Microscopy Research and Technique, vol.59, issue.4, pp.260-266, 2006. ,
DOI : 10.1111/j.1365-2818.1990.tb04774.x
EM reconstruction algorithms for emission and transmission tomography, J. Comput. Assist. Tomo, vol.8, issue.2, pp.306-316, 1984. ,
Parallelizable Bayesian tomography algorithms with rapid, guaranteed convergence, IEEE Transactions on Image Processing, vol.9, issue.10, pp.1745-1759, 2000. ,
DOI : 10.1109/83.869186
URL : http://dynamo.ecn.purdue.edu/~bouman/publications/./orig-pdf/ip12.pdf
Dynamic PET Reconstruction Using Wavelet Regularization With Adapted Basis Functions, IEEE Transactions on Medical Imaging, vol.27, issue.7, pp.943-959, 2008. ,
DOI : 10.1109/TMI.2008.923698
URL : https://infoscience.epfl.ch/record/130357/files/verhaeghe0801.pdf
Parallel algorithm and hybrid regularization for dynamic PET reconstruction, IEEE Nuclear Science Symposuim & Medical Imaging Conference, p.5, 2010. ,
DOI : 10.1109/NSSMIC.2010.5874223
URL : https://hal.archives-ouvertes.fr/hal-00733493
Inverse problems in atmospheric science and their application, Journal of Physics: Conference Series, vol.12, issue.1, p.4557, 2005. ,
DOI : 10.1088/1742-6596/12/1/005
Tikhonov regularization of incorrectly posed problems, Soviet Mathematics Doklady, vol.4, pp.1624-1627, 1963. ,
Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, Readings in Computer Vision, pp.564-584, 1987. ,
Proximal splitting methods in signal processing, " in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212, 2011. ,
Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2011. ,
DOI : 10.1007/978-3-319-48311-5
Wavelet-Based Image Deconvolution and Reconstruction, 2016. ,
DOI : 10.1109/83.392335
URL : https://hal.archives-ouvertes.fr/hal-01164833
Jump-Sparse and Sparse Recovery Using Potts Functionals, IEEE Transactions on Signal Processing, vol.62, issue.14, pp.3654-3666, 2014. ,
DOI : 10.1109/TSP.2014.2329263
URL : http://bigwww.epfl.ch/publications/storath1401.pdf
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
Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989. ,
DOI : 10.1109/TPAMI.1984.4767596
URL : https://dash.harvard.edu/bitstream/handle/1/3637121/Mumford_OptimalApproxPiece.pdf?sequence=1
Discrete Total Variation: New Definition and Minimization, SIAM Journal on Imaging Sciences, vol.10, issue.3, pp.1258-1290, 2017. ,
DOI : 10.1137/16M1075247
URL : https://hal.archives-ouvertes.fr/hal-01309685
Image smoothing via L0 gradient minimization, ACM Transactions on Graphics, vol.30, p.174, 2011. ,
Joint image reconstruction and segmentation using the Potts model, Inverse Problems, vol.31, issue.2, p.25003, 2015. ,
DOI : 10.1088/0266-5611/31/2/025003
URL : http://bigwww.epfl.ch/publications/storath1501.pdf
Real-Time Minimization of the Piecewise Smooth Mumford-Shah Functional, Proc. European Conference on Computer Vision, pp.127-141, 2014. ,
DOI : 10.1007/978-3-319-10605-2_9
Discretized Convex Relaxations for the Piecewise Smooth Mumford-Shah Model, Int. Conf. on Energy Minimization Methods in Computer Vision and Pattern Recognition, 2017. ,
DOI : 10.1007/978-3-642-33783-3_28
Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models, SIAM Journal on Applied Mathematics, vol.66, issue.5, pp.1632-1648, 2006. ,
DOI : 10.1137/040615286
Fast Global Minimization of the Active Contour/Snake Model, Journal of Mathematical Imaging and Vision, vol.7, issue.3, pp.151-167, 2007. ,
DOI : 10.1007/b98879
Regularized Non-local Total Variation and Application in Image Restoration, Journal of Mathematical Imaging and Vision, vol.3, issue.3, pp.296-317, 2017. ,
DOI : 10.1137/090746379
URL : https://hal.archives-ouvertes.fr/hal-01342111
Image restoration and segmentation using the Ambrosio-Tortorelli functional and Discrete Calculus, 2016 23rd International Conference on Pattern Recognition (ICPR), 2016. ,
DOI : 10.1109/ICPR.2016.7899836
URL : https://hal.archives-ouvertes.fr/hal-01379993
Numerical Implementation of the Ambrosio-Tortorelli Functional Using Discrete Calculus and Application to Image Restoration and Inpainting, Proc. 1st Workshop on Reproducible Research in Pattern Recognition (RRPR2016), 2016. ,
DOI : 10.1109/ICIP.2009.5414042
Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Mathematical Programming, vol.4, issue.1-2, pp.459-494, 2014. ,
DOI : 10.1007/BF01584660
URL : https://hal.archives-ouvertes.fr/hal-00916090
Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-??ojasiewicz Inequality, Mathematics of Operations Research, vol.35, issue.2, pp.438-457, 2010. ,
DOI : 10.1287/moor.1100.0449
Semi-blind image restoration via Mumford-Shah regularization, IEEE Transactions on Image Processing, vol.15, issue.2, pp.483-493, 2006. ,
DOI : 10.1109/TIP.2005.863120
A Variational Framework for Simultaneous Motion Estimation and Restoration of Motion-Blurred Video, 2007 IEEE 11th International Conference on Computer Vision, pp.1-8, 2007. ,
DOI : 10.1109/ICCV.2007.4409009
Nonlocal Mumford-Shah Regularizers for Color Image Restoration, IEEE Transactions on Image Processing, vol.20, issue.6, pp.1583-1598, 2011. ,
DOI : 10.1109/TIP.2010.2092433
Hybrid regularization for data restoration in the presence of Poisson noise, Proc. Eur. Sig. Proc. Conference, pp.1394-1398, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00621941
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods, Journal of Mathematical Imaging and Vision, vol.11, issue.11, pp.168-184, 2010. ,
DOI : 10.1137/1.9780898718324
URL : http://www.mathematik.uni-kl.de/uploads/tx_sibibtex/mult_noise_drs_rev_01.pdf
Approximation of functional depending on jumps by elliptic functional via t-convergence, Communications on Pure and Applied Mathematics, vol.17, issue.8, pp.999-1036, 1990. ,
DOI : 10.1080/01621459.1987.10478393
On the approximation of free discontinuity problems, Boll. Un. Mat. Ital, vol.6, pp.105-123, 1992. ,
Mumford and Shah model and its applications to image segmentation and image restoration, Handbook of mathematical methods in imaging, pp.1095-1157, 2011. ,
DOI : 10.1007/978-0-387-92920-0_25
A common framework for curve evolution, segmentation and anisotropic diffusion, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.136-142, 1996. ,
DOI : 10.1109/CVPR.1996.517065
URL : http://www.math.neu.edu/~shah/papers/commonframewk95.pdf
Free-discontinuity problems via functionals involving the L1-norm of the gradient and their approximations, Interfaces and free boundaries, pp.17-37, 1999. ,
DOI : 10.4171/IFB/2
Proximal splitting methods in signal processing, " in Fixed-point algorithms for inverse problems in science and engineering, pp.185-212, 2011. ,
Optimization with Sparsity-Inducing Penalties, Foundations and Trends?? in Machine Learning, vol.4, issue.1, pp.1-106, 2012. ,
DOI : 10.1561/2200000015
URL : https://hal.archives-ouvertes.fr/hal-00613125
Image Quality Assessment: From Error Visibility to Structural Similarity, IEEE Transactions on Image Processing, vol.13, issue.4, pp.600-612, 2004. ,
DOI : 10.1109/TIP.2003.819861
URL : http://www.cns.nyu.edu/~zwang/files/papers/ssim.pdf
Distribution de la flore alpine dans le bassin des Dranses et dans quelques régions voisines, Bull. Soc. Vaudoise Sci. Nat, vol.37, pp.241-272, 1901. ,
On Information and Sufficiency, The annals of mathematical statistics, pp.79-86, 1951. ,
DOI : 10.1214/aoms/1177729694
URL : http://doi.org/10.1214/aoms/1177729694