DEGRADATION: STD. DEVIATION = 5, DECIMATION = 90%. ( " SPEED UP " IS THE RATIO BETWEEN " DIRECT " AND " EPIGRAPHICAL " TIMES) ? SNR (dB) ? M-SNR (dB) REFERENCES ,
Compressed Sensing and Redundant Dictionaries, IEEE Transactions on Information Theory, vol.54, issue.5, pp.2210-2219, 2008. ,
DOI : 10.1109/TIT.2008.920190
Compressive Sensing by Random Convolution, SIAM Journal on Imaging Sciences, vol.2, issue.4, pp.1098-1128, 2009. ,
DOI : 10.1137/08072975X
Hyperspectral image compressed sensing via low-rank and joint-sparse matrix recovery, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2012. ,
DOI : 10.1109/ICASSP.2012.6288484
URL : https://hal.archives-ouvertes.fr/hal-00705915
Inpainting and Zooming Using Sparse Representations, The Computer Journal, vol.52, issue.1, pp.64-79, 2009. ,
DOI : 10.1093/comjnl/bxm055
URL : https://hal.archives-ouvertes.fr/hal-00091746
Missing-Area Reconstruction in Multispectral Images Under a Compressive Sensing Perspective, IEEE Transactions on Geoscience and Remote Sensing, vol.51, issue.7, pp.3998-4008, 2013. ,
DOI : 10.1109/TGRS.2012.2227329
URL : https://hal.archives-ouvertes.fr/hal-01058015
Compressed Sensing-Based Inpainting of Aqua Moderate Resolution Imaging Spectroradiometer Band 6 Using Adaptive Spectrum-Weighted Sparse Bayesian Dictionary Learning, IEEE Transactions on Geoscience and Remote Sensing, vol.52, issue.2, pp.894-906, 2014. ,
DOI : 10.1109/TGRS.2013.2245509
A super-resolution reconstruction algorithm for hyperspectral images, Signal Processing, vol.92, issue.9, pp.2082-2096, 2012. ,
DOI : 10.1016/j.sigpro.2012.01.020
Parametric Blur Estimation for Blind Restoration of Natural Images: Linear Motion and Out-of-Focus, IEEE Transactions on Image Processing, vol.23, issue.1, pp.466-477, 2014. ,
DOI : 10.1109/TIP.2013.2286328
An epigraphical convex optimization approach for multicomponent image restoration using non-local structure tensor, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, 2013. ,
DOI : 10.1109/ICASSP.2013.6637873
URL : https://hal.archives-ouvertes.fr/hal-00826003
Hyperspectral Image Denoising Employing a Spectral–Spatial Adaptive Total Variation Model, IEEE Transactions on Geoscience and Remote Sensing, vol.50, issue.10, pp.3660-3677, 2012. ,
DOI : 10.1109/TGRS.2012.2185054
Inpainting for Remotely Sensed Images With a Multichannel Nonlocal Total Variation Model, IEEE Transactions on Geoscience and Remote Sensing, vol.52, issue.1 ,
DOI : 10.1109/TGRS.2012.2237521
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
Image Restoration Subject to a Total Variation Constraint, IEEE Transactions on Image Processing, vol.13, issue.9, pp.1213-1222, 2004. ,
DOI : 10.1109/TIP.2004.832922
URL : https://hal.archives-ouvertes.fr/hal-00621804
Total Generalized Variation, SIAM Journal on Imaging Sciences, vol.3, issue.3, pp.492-526, 2010. ,
DOI : 10.1137/090769521
Second-order total Generalized Variation constraint, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014. ,
DOI : 10.1109/ICASSP.2014.6854541
Higher Degree Total Variation (HDTV) Regularization for Image Recovery, IEEE Transactions on Image Processing, vol.21, issue.5, pp.2559-2571, 2012. ,
DOI : 10.1109/TIP.2012.2183143
Generalized Higher Degree Total Variation (HDTV) Regularization, IEEE Transactions on Image Processing, vol.23, issue.6, pp.2423-2435, 2014. ,
DOI : 10.1109/TIP.2014.2315156
Nonlocal Operators with Applications to Image Processing, Multiscale Modeling & Simulation, vol.7, issue.3, p.1005, 2009. ,
DOI : 10.1137/070698592
Adaptive Regularization of the NL-Means: Application to Image and Video Denoising, IEEE Transactions on Image Processing, vol.23, issue.8, 2014. ,
DOI : 10.1109/TIP.2014.2329448
URL : https://hal.archives-ouvertes.fr/hal-00854830
Nonlocal Regularization of Inverse Problems: A Unified Variational Framework, IEEE Transactions on Image Processing, vol.22, issue.8, pp.3192-3203, 2013. ,
DOI : 10.1109/TIP.2012.2216278
A wavelet tour of signal processing, 1997. ,
Building robust wavelet estimators for multicomponent images using Stein's principle, IEEE Transactions on Image Processing, vol.14, issue.11, pp.1814-1830, 2005. ,
DOI : 10.1109/TIP.2005.857247
A Nonlinear Stein-Based Estimator for Multichannel Image Denoising, IEEE Transactions on Signal Processing, vol.56, issue.8, pp.3855-3870, 2008. ,
DOI : 10.1109/TSP.2008.921757
URL : https://hal.archives-ouvertes.fr/hal-00617318
Wavelet transform for the denoising of multivariate images Proximal algorithms for multicomponent image recovery problems, Multivariate Image Processing, C. Collet, J. Chanussot, and, pp.203-237, 2010. ,
Pointwise Shape-Adaptive DCT for High-Quality Denoising and Deblocking of Grayscale and Color Images, IEEE Transactions on Image Processing, vol.16, issue.5, pp.1395-1411, 2007. ,
DOI : 10.1109/TIP.2007.891788
<tex>$rm K$</tex>-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation, IEEE Transactions on Signal Processing, vol.54, issue.11, pp.4311-4322, 2006. ,
DOI : 10.1109/TSP.2006.881199
On the Role of Sparse and Redundant Representations in Image Processing, Proceedings of the IEEE, vol.98, issue.6, pp.972-982, 2010. ,
DOI : 10.1109/JPROC.2009.2037655
URL : https://hal.archives-ouvertes.fr/inria-00568893
Recovering quantitative remote sensing products contaminated by thick clouds and shadows using multitemporal dictionary learning, IEEE Trans. Geosci ,
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering, IEEE Transactions on Image Processing, vol.16, issue.8, pp.2080-2095, 2007. ,
DOI : 10.1109/TIP.2007.901238
Nonlocal Transform-Domain Filter for Volumetric Data Denoising and Reconstruction, IEEE Transactions on Image Processing, vol.22, issue.1, pp.119-133, 2013. ,
DOI : 10.1109/TIP.2012.2210725
BM3D Frames and Variational Image Deblurring, IEEE Transactions on Image Processing, vol.21, issue.4, pp.1715-1728, 2012. ,
DOI : 10.1109/TIP.2011.2176954
Color TV: total variation methods for restoration of vector-valued images, IEEE Transactions on Image Processing, vol.7, issue.3, pp.304-309, 1998. ,
DOI : 10.1109/83.661180
Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization, MPS- SIAM Series on Optimization, 2006. ,
DOI : 10.1137/1.9781611973488
A duality based approach for realtime TV-L1 optical flow, Proc. DAGM Symposium, pp.214-223, 2007. ,
Projected Gradient Based Color Image Decomposition, Scale Space and Variational Methods in Computer Vision, pp.295-306, 2009. ,
DOI : 10.1007/s11263-006-4331-z
A note on the gradient of a multi-image, Computer Vision, Graphics, and Image Processing, vol.33, issue.1, pp.116-125, 1986. ,
DOI : 10.1016/0734-189X(86)90223-9
Anisotropic diffusion of multivalued images with applications to color filtering, IEEE Transactions on Image Processing, vol.5, issue.11, pp.1582-1586, 1996. ,
DOI : 10.1109/83.541429
A general framework for low level vision, IEEE Transactions on Image Processing, vol.7, issue.3, pp.310-318, 1998. ,
DOI : 10.1109/83.661181
Coherence-enhancing diffusion of colour images, Image and Vision Computing, vol.17, issue.3-4, pp.201-212, 1999. ,
DOI : 10.1016/S0262-8856(98)00102-4
Constrained and unconstrained PDE's for vector image restoration, Scandinavian Conference on Image Analysis, 2001. ,
Fast dual minimization of the vectorial total variation norm and applications to color image processing, Inverse Problems and Imaging, vol.2, issue.4, pp.455-484, 2008. ,
DOI : 10.3934/ipi.2008.2.455
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
The Natural Vectorial Total Variation Which Arises from Geometric Measure Theory, SIAM Journal on Imaging Sciences, vol.5, issue.2, pp.537-563, 2012. ,
DOI : 10.1137/110823766
Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems, Scale-Space and Variational Methods in Computer Vision, pp.48-60, 2013. ,
DOI : 10.1007/978-3-642-38267-3_5
Image Restoration by the Method of Convex Projections: Part 1ߞTheory, IEEE Transactions on Medical Imaging, vol.1, issue.2, pp.81-94, 1982. ,
DOI : 10.1109/TMI.1982.4307555
The feasible solution in signal restoration, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.32, issue.2, pp.201-212, 1984. ,
DOI : 10.1109/TASSP.1984.1164297
Inconsistent signal feasibility problems: least-squares solutions in a product space, IEEE Transactions on Signal Processing, vol.42, issue.11, pp.2955-2966, 1994. ,
DOI : 10.1109/78.330356
Filtered Variation method for denoising and sparse signal processing, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.3329-3332, 2012. ,
DOI : 10.1109/ICASSP.2012.6288628
-divergence constraints, Inverse Problems, vol.29, issue.3, p.29, 2013. ,
DOI : 10.1088/0266-5611/29/3/035007
URL : https://hal.archives-ouvertes.fr/hal-00868432
Democratic representations, 2014. ,
Convex analysis and minimization algorithms, Part I : Fundamentals, 1996. ,
Hyperspectral Image Representation and Processing With Binary Partition Trees, IEEE Transactions on Image Processing, vol.22, issue.4, pp.1430-1443, 2013. ,
DOI : 10.1109/TIP.2012.2231687
URL : https://hal.archives-ouvertes.fr/hal-00798351
Image restoration in astronomy: a Bayesian perspective, IEEE Signal Processing Magazine, vol.18, issue.2, pp.11-29, 2001. ,
DOI : 10.1109/79.916318
The colored revolution of bioimaging, IEEE Signal Processing Magazine, vol.23, issue.3, pp.20-31, 2006. ,
DOI : 10.1109/MSP.2006.1628875
Spectral–Spatial Classification of Hyperspectral Data Based on a Stochastic Minimum Spanning Forest Approach, IEEE Transactions on Image Processing, vol.21, issue.4, pp.2008-2021, 2012. ,
DOI : 10.1109/TIP.2011.2175741
Vector-valued image regularization with PDEs: a common framework for different applications, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.27, issue.4, pp.506-517, 2005. ,
DOI : 10.1109/TPAMI.2005.87
Anisotropic Diffusion in the Hypercube, IEEE Transactions on Geoscience and Remote Sensing, vol.45, issue.5, pp.1386-1398, 2007. ,
DOI : 10.1109/TGRS.2007.894569
Accurate Implementation of Anisotropic Diffusion in the Hypercube, IEEE Geoscience and Remote Sensing Letters, vol.7, issue.4 ,
DOI : 10.1109/LGRS.2010.2054062
Survey of hyperspectral image denoising methods based on tensor decompositions, EURASIP Journal on Advances in Signal Processing, vol.2013, issue.1, 2013. ,
DOI : 10.1186/1687-6180-2013-186
URL : https://hal.archives-ouvertes.fr/hal-01281026
Robust principal component analysis?, Journal of the ACM, vol.58, issue.3, pp.1-1137, 2011. ,
DOI : 10.1145/1970392.1970395
Robust Matrix Decomposition With Sparse Corruptions, IEEE Transactions on Information Theory, vol.57, issue.11, pp.7221-7234, 2011. ,
DOI : 10.1109/TIT.2011.2158250
Exploiting structural complexity for robust and rapid hyperspectral imaging, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, 2013. ,
DOI : 10.1109/ICASSP.2013.6638043
Joint Bayesian Endmember Extraction and Linear Unmixing for Hyperspectral Imagery, IEEE Transactions on Signal Processing, vol.57, issue.11, pp.4355-4368, 2009. ,
DOI : 10.1109/TSP.2009.2025797
URL : https://hal.archives-ouvertes.fr/hal-00548758
Fast Constrained Least Squares Spectral Unmixing Using Primal-Dual Interior-Point Optimization, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol.7, issue.1, pp.59-69, 2013. ,
DOI : 10.1109/JSTARS.2013.2266732
URL : https://hal.archives-ouvertes.fr/hal-00828013
A signal processing perspective on hyperspectral unmixing, IEEE Trans. Signal Process, 2014. ,
On the Early History of the Singular Value Decomposition, SIAM Review, vol.35, issue.4, pp.551-566, 1993. ,
DOI : 10.1137/1035134
A convex regularizer for reducing color artifact in color image recovery, CVPR, 2013. ,
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 Review of Image Denoising Algorithms, with a New One, Multiscale Modeling & Simulation, vol.4, issue.2, pp.490-530, 2005. ,
DOI : 10.1137/040616024
URL : https://hal.archives-ouvertes.fr/hal-00271141
Foveated self-similarity in nonlocal image filtering, Human Vision and Electronic Imaging XVII, 2012. ,
DOI : 10.1117/12.912217
Nonlocal Linear Image Regularization and Supervised Segmentation, Multiscale Modeling & Simulation, vol.6, issue.2, pp.595-630, 2007. ,
DOI : 10.1137/060669358
Probing the Pareto Frontier for Basis Pursuit Solutions, SIAM Journal on Scientific Computing, vol.31, issue.2, pp.890-912, 2008. ,
DOI : 10.1137/080714488
An efficient projection for 1,? regularization, International Conference on Machine Learning, pp.857-864, 2009. ,
Epigraphical projection and proximal tools for solving constrained convex optimization problems Signal Image Video Process Epigraphical projection for solving least squares Anscombe transformed constrained optimization problems, Scale-Space and Variational Methods in Computer Vision, pp.125-136, 2013. ,
Signal reconstruction framework based on Projections onto Epigraph Set of a Convex cost function (PESC), 2014. ,
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Communications on Pure and Applied Mathematics, vol.58, issue.11, pp.1413-1457, 2004. ,
DOI : 10.1002/cpa.20042
A variational formulation for frame-based inverse problems, Inverse Problems, vol.23, issue.4, pp.1495-1518, 2007. ,
DOI : 10.1088/0266-5611/23/4/008
URL : https://hal.archives-ouvertes.fr/hal-00621883
A Douglas???Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery, IEEE Journal of Selected Topics in Signal Processing, vol.1, issue.4, pp.564-574, 2007. ,
DOI : 10.1109/JSTSP.2007.910264
URL : https://hal.archives-ouvertes.fr/hal-00621820
Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems, IEEE Journal of Selected Topics in Signal Processing, vol.1, issue.4, pp.586-598, 2007. ,
DOI : 10.1109/JSTSP.2007.910281
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, SIAM Journal on Imaging Sciences, vol.2, issue.1, pp.183-202, 2009. ,
DOI : 10.1137/080716542
Subspace Correction Methods for Total Variation and $\ell_1$-Minimization, SIAM Journal on Numerical Analysis, vol.47, issue.5, pp.3397-3428, 2009. ,
DOI : 10.1137/070710779
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods, Journal of Mathematical Imaging and Vision, vol.11, issue.11, pp.168-184, 2010. ,
DOI : 10.1007/s10851-009-0179-5
Proximal splitting methods in signal processing, " in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212 ,
A parallel inertial proximal optimization method, Pac. J. Optim, vol.8, issue.2, pp.273-305, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00790702
A proximal-based decomposition method for convex minimization problems, Mathematical Programming, vol.29, issue.1-3, pp.81-101, 1994. ,
DOI : 10.1007/BF01582566
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science, SIAM Journal on Imaging Sciences, vol.3, issue.4, pp.1015-1046, 2010. ,
DOI : 10.1137/09076934X
A First-Order Primal-Dual Algorithm for Convex Problems with??Applications to Imaging, Journal of Mathematical Imaging and Vision, vol.60, issue.5, pp.120-145, 2011. ,
DOI : 10.1007/s10851-010-0251-1
URL : https://hal.archives-ouvertes.fr/hal-00490826
A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality, SIAM Journal on Optimization, vol.21, issue.4, pp.1230-1250, 2011. ,
DOI : 10.1137/10081602X
Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators Set-Valued Var, Anal, vol.20, issue.2, pp.307-330, 2012. ,
A splitting algorithm for dual monotone inclusions involving cocoercive operators, Adv. Comput. Math, vol.38, issue.3, pp.667-681, 2013. ,
A Primal???Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms, Journal of Optimization Theory and Applications, vol.23, issue.1???2, pp.460-479, 2012. ,
DOI : 10.1007/s10957-012-0245-9
URL : https://hal.archives-ouvertes.fr/hal-00609728
A primal???dual fixed point algorithm for convex separable minimization with applications to image restoration, Inverse Problems, vol.29, issue.2, 2013. ,
DOI : 10.1088/0266-5611/29/2/025011
Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems, IEEE Signal Processing Magazine, vol.32, issue.6, 2014. ,
DOI : 10.1109/MSP.2014.2377273
URL : https://hal.archives-ouvertes.fr/hal-01246610
Proximit?? et dualit?? dans un espace hilbertien, Bulletin de la Société mathématique de France, vol.79, pp.273-299, 1965. ,
DOI : 10.24033/bsmf.1625
On the Douglas???Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, pp.293-318, 1992. ,
DOI : 10.1007/BF01581204
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
An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems, IEEE Transactions on Image Processing, vol.20, issue.3, pp.681-695, 2011. ,
DOI : 10.1109/TIP.2010.2076294
Parallel alternating direction multiplier decomposition of convex programs, Journal of Optimization Theory and Applications, vol.10, issue.1, pp.39-62, 1994. ,
DOI : 10.1007/BF02196592
A proximal decomposition method for solving convex variational inverse problems, Inverse Problems, vol.24, issue.6, 2008. ,
DOI : 10.1088/0266-5611/24/6/065014
URL : https://hal.archives-ouvertes.fr/hal-00692901
Fast Image Recovery Using Variable Splitting and Constrained Optimization, IEEE Transactions on Image Processing, vol.19, issue.9, pp.2345-2356, 2010. ,
DOI : 10.1109/TIP.2010.2047910
Relaxing Tight Frame Condition in Parallel Proximal Methods for Signal Restoration, IEEE Transactions on Signal Processing, vol.60, issue.2, pp.968-973, 2012. ,
DOI : 10.1109/TSP.2011.2173684
URL : https://hal.archives-ouvertes.fr/hal-00692256
Group sparsity with overlapping partition functions, Proc. Eur. Sig. and Image Proc. Conference, 2011. ,
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing, SIAM Journal on Scientific Computing, vol.31, issue.3 ,
DOI : 10.1137/070696143
URL : https://hal.archives-ouvertes.fr/inria-00166096
Total Variation Projection With First Order Schemes, IEEE Transactions on Image Processing, vol.20, issue.3, pp.657-669, 2011. ,
DOI : 10.1109/TIP.2010.2072512
URL : https://hal.archives-ouvertes.fr/hal-00401251
Joint demosaicking and denoising by total variation minimization, 2012 19th IEEE International Conference on Image Processing, 2012. ,
DOI : 10.1109/ICIP.2012.6467476
URL : https://hal.archives-ouvertes.fr/hal-00598807
A generic proximal algorithm for convex optimization application to total variation minimization, IEEE Signal Proc. Letters, pp.1054-1057, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01120544
Fast projection onto the simplex and the l1 ball, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01056171
She received the Ph.D. degree in signal and image processing from the Université Paris-Est Marne-la-Vallée, France, in 2010. From 2010 to 2011, she was a Postdoctoral research associate with the Laboratoire IMS France, working on the topic of tomographic reconstruction from a limited number of projections. Since 2012, she is a CNRS researcher in the Signal Processing Team of the Laboratoire de Physique de l'ENS de Lyon. Her activity is focused on inverse problems, non-smooth convex optimization, mode decomposition, and texture analysis ,