Linear Convergence Rates for Gauge Regularization ,
Stein Unbiased GrAdient Risk estimates (SUGAR) for multiple parameter selection, 2014. ,
Partly Smooth Regularization of Inverse Problems, 2014. ,
The Degrees of Freedom of Partly Smooth Gauge Regularizers, 2014. ,
Model Selection with Piecewise Regular Gauges, 2013. ,
Robust Sparse Analysis Regularization, IEEE Transactions on Information Theory, vol.59, issue.4, pp.2001-2016, 2013. ,
DOI : 10.1109/TIT.2012.2233859
URL : https://hal.archives-ouvertes.fr/hal-00627452
Local behavior of sparse analysis regularization: Applications to risk estimation, Sampling Theory and Applications, pp.433-451, 2013. ,
DOI : 10.1016/j.acha.2012.11.006
URL : https://hal.archives-ouvertes.fr/hal-00687751
Stable Recovery with Analysis Decomposable Priors, Sampling Theory and Applications, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00926727
The degrees of freedom of the Group Lasso for a General Design, Signal Processing with Adaptive Sparse Structured Representations (SPARS), 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00768896
Proximal Splitting Derivatives for Risk Estimation, New Computational Methods for Inverse Problems, p.2012 ,
DOI : 10.1088/1742-6596/386/1/012003
URL : https://hal.archives-ouvertes.fr/hal-00670213
Risk estimation for matrix recovery with spectral regularization, International Conference on Machine Learning Workshop (ICML), 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00695326
Degrees of Freedom of the Group Lasso, International Conference on Machine Learning Workshop (ICML). 2012 ,
URL : https://hal.archives-ouvertes.fr/hal-00695292
Unbiased risk estimation for sparse analysis regularization, 2012 19th IEEE International Conference on Image Processing ,
DOI : 10.1109/ICIP.2012.6467544
URL : https://hal.archives-ouvertes.fr/hal-00662718
Reconstruction Stable par Régularisation Décomposable Analyse, GRETSI. 2013 ,
Partly Smooth Regularization of Inverse Problems, 2014. ,
The Degrees of Freedom of Partly Smooth Gauge Regularizers, 2014. ,
Model Selection with Piecewise Regular Gauges, 2013. ,
Robust Sparse Analysis Regularization, IEEE Transactions on Information Theory, vol.59, issue.4, pp.2001-2016, 2013. ,
DOI : 10.1109/TIT.2012.2233859
URL : https://hal.archives-ouvertes.fr/hal-00627452
Local behavior of sparse analysis regularization: Applications to risk estimation, Applied and Computational Harmonic Analysis, vol.35, issue.3, pp.433-451, 2000. ,
DOI : 10.1016/j.acha.2012.11.006
URL : https://hal.archives-ouvertes.fr/hal-00687751
Set-Valued Analysis, Modern Birkhauser Classics. Birkhauser, vol.117, p.49, 2009. ,
Asymptotic cones and functions in optimization and variational inequalities, pp.51-53, 2003. ,
Convex analysis and monotone operator theory in Hilbert spaces, p.225, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00643354
Perturbation analysis of optimization problems . Springer Series in Operations Research and Financial Engineering, pp.31-199, 2000. ,
Convex analysis and nonlinear optimization: theory and examples, 2010. ,
Convex optimization, p.22, 2004. ,
Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory, Monograph Series. IMS, vol.204, p.188, 1986. ,
Statistics for high-dimensional data: methods, theory and applications, p.188, 2011. ,
Asymptotic Theory of Statistics and Probability, p.204, 2008. ,
Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, 1992. ,
Implicit functions and solution mappings: A view from variational analysis, p.53, 2009. ,
Tame topology and o-minimal structures, Math. Soc. Lecture Note, pp.70-71, 1998. ,
Analyse convexe et problemes variationelles, 1974. ,
Sparse and redundant representations: from theory to applications in signal and image processing, 2010. ,
DOI : 10.1007/978-1-4419-7011-4
Measure theory and fine properties of functions, p.214, 1992. ,
Fundamentals of computerized tomography: image reconstruction from projections, 2009. ,
DOI : 10.1007/978-1-84628-723-7
Convex Analysis And Minimization Algorithms, pp.60-62, 2001. ,
DOI : 10.1007/978-3-662-02796-7
Matrix analysis, p.67, 2012. ,
Smooth manifolds, p.58, 2003. ,
A wavelet tour of signal processing. Third, pp.17-20, 2009. ,
Wavelets and operators, p.20, 1992. ,
Interior-point polynomial algorithms in convex programming, SIAM, 1994. ,
DOI : 10.1137/1.9781611970791
Radiology of the Skull and Brain: Technical aspects of computed tomography, Radiology of the Skull and Brain. Mosby, 1981. ,
Introduction to optimization. Optimization Software, 1987. ,
Statistical Image Processing techniques for Noisy Images -An application Oriented Approach, Kluwer, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00080004
Variational analysis, 1998. ,
DOI : 10.1007/978-3-642-02431-3
Convex analysis, pp.61-76, 1996. ,
DOI : 10.1515/9781400873173
Variational methods in imaging, pp.155-159, 2009. ,
Sparse image and signal processing: wavelets, curvelets, morphological diversity, p.15, 2010. ,
DOI : 10.1017/CBO9780511730344
URL : https://hal.archives-ouvertes.fr/hal-01132685
Solutions of ill-posed problems, 1977. ,
The elements of statistical learning. Second, 2009. ,
Collected works, 1961. ,
Convex analysis in general vector spaces, World Scientific, 2002. ,
DOI : 10.1142/5021
Optical Sectioning Microscopy: Cellular Architecture in Three Dimensions, Annual Review of Biophysics and Bioengineering, vol.13, issue.1, pp.191-219, 1984. ,
DOI : 10.1146/annurev.bb.13.060184.001203
Short term spectral analysis, synthesis, and modification by discrete Fourier transform, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.25, issue.3, pp.235-238, 1977. ,
DOI : 10.1109/TASSP.1977.1162950
Living on the edge: A geometric theory of phase transitions in convex optimization, p.239, 2013. ,
Consistency of the group Lasso and multiple kernel learning, The Journal of Machine Learning Research, vol.9, issue.148, pp.1179-1225, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00164735
Certifying the Restricted Isometry Property is Hard, IEEE Transactions on Information Theory, vol.59, issue.6, pp.3448-3450, 2013. ,
DOI : 10.1109/TIT.2013.2248414
Risk bounds for model selection via penalization, Probability Theory and Related Fields, vol.113, issue.3, pp.301-413, 1999. ,
DOI : 10.1007/s004400050210
Gradient-based algorithms with applications to signal-recovery problems, Convex Optimization in Signal Processing and Communications, 2009. ,
DOI : 10.1017/CBO9780511804458.003
Iterative methods for image deblurring, Proceedings of the IEEE, vol.78, issue.5, pp.856-883, 1990. ,
DOI : 10.1109/5.53403
From model selection to adaptive estimation Chap. 4 in Festschrift for Lucien Le Cam, pp.55-87, 1997. ,
Compressed Sensing in Astronomy, Selected Topics in Signal Processing, pp.718-726, 2008. ,
DOI : 10.1109/JSTSP.2008.2005337
Handbook of Image and Video Processing, Chap. Image Noise Models in, 2005. ,
Beyond coherence: Recovering structured time???frequency representations, Applied and Computational Harmonic Analysis, vol.24, issue.1, pp.120-128, 2008. ,
DOI : 10.1016/j.acha.2007.09.002
URL : https://hal.archives-ouvertes.fr/inria-00544766
Total Generalized Variation, SIAM Journal on Imaging Sciences, vol.3, issue.3, pp.492-526, 2010. ,
DOI : 10.1137/090769521
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.378.6330
Inverse problems in spaces of measures, ESAIM: Control, Optimisation and Calculus of Variations, vol.19, issue.1, pp.190-218, 2013. ,
DOI : 10.1051/cocv/2011205
Honest variable selection in linear and logistic regression models via ???1 and ???1+???2 penalization, Electronic Journal of Statistics, vol.2, issue.0, pp.1153-1194, 2008. ,
DOI : 10.1214/08-EJS287
Convergence rates of convex variational regularization, Inverse Problems, vol.20, issue.5, pp.1411-1437, 2004. ,
DOI : 10.1088/0266-5611/20/5/005
inequality approach, The Annals of Statistics, vol.27, issue.3, pp.898-924, 1999. ,
DOI : 10.1214/aos/1018031262
Incorporating information on neighbouring coefficients into wavelet estimation, Sankhya: The Indian Journal of Statistics, Series B, pp.127-148, 2001. ,
Compressed sensing with coherent and redundant dictionaries, Applied and Computational Harmonic Analysis, vol.31, issue.1, pp.59-73, 2011. ,
DOI : 10.1016/j.acha.2010.10.002
Towards a Mathematical Theory of Super-resolution, Communications on Pure and Applied Mathematics, vol.52, issue.3, pp.906-956, 2013. ,
DOI : 10.1002/cpa.21455
Matrix Completion With Noise, Proceedings of the IEEE, vol.98, issue.6, pp.925-936, 2010. ,
DOI : 10.1109/JPROC.2009.2035722
A Probabilistic and RIPless Theory of Compressed Sensing Information Theory, IEEE Transactions on, vol.57, issue.11, pp.7235-7254, 2011. ,
Simple bounds for recovering low-complexity models, Mathematical Programming, vol.52, issue.3, pp.577-589, 2013. ,
DOI : 10.1007/s10107-012-0540-0
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, vol.52, issue.2, pp.489-509, 2006. ,
DOI : 10.1109/TIT.2005.862083
Decoding by linear programming Information Theory, IEEE Transactions on, vol.51, issue.12, pp.4203-4215, 2005. ,
The Discontinuity Set of Solutions of the TV Denoising Problem and Some Extensions, Multiscale Modeling & Simulation, vol.6, issue.3, pp.879-894, 2007. ,
DOI : 10.1137/070683003
An Introduction to Total Variation for Image Analysis, Theoretical Foundations and Numerical Methods for Sparse Recovery. De Gruyter, p.16, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00437581
Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage, IEEE Transactions on Image Processing, vol.7, issue.3, pp.319-335, 1998. ,
DOI : 10.1109/83.661182
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.4107
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
Image sequence filtering in quantum-limited noise with applications to low-dose fluoroscopy, IEEE Transactions on Medical Imaging, vol.12, issue.3, pp.610-621, 1993. ,
DOI : 10.1109/42.241890
The Convex Geometry of Linear Inverse Problems, Foundations of Computational Mathematics, vol.1, issue.10, pp.805-849, 2012. ,
DOI : 10.1007/s10208-012-9135-7
Theoretical Results on Sparse Representations of Multiple-Measurement Vectors, IEEE Transactions on Signal Processing, vol.54, issue.12, pp.4634-4643, 2006. ,
DOI : 10.1109/TSP.2006.881263
Atomic Decomposition by Basis Pursuit, SIAM Journal on Scientific Computing, vol.20, issue.1, pp.33-61, 1999. ,
DOI : 10.1137/S1064827596304010
Stein block thresholding for image denoising, Applied and Computational Harmonic Analysis, vol.28, issue.1, pp.67-88, 2010. ,
DOI : 10.1016/j.acha.2009.07.003
URL : https://hal.archives-ouvertes.fr/hal-00323319
Stein block thresholding for wavelet-based image deconvolution, Electronic Journal of Statistics, vol.4, issue.0, pp.415-435, 2010. ,
DOI : 10.1214/09-EJS550
URL : https://hal.archives-ouvertes.fr/hal-00436661
Homogeneous Penalizers and Constraints in Convex Image Restoration, Journal of Mathematical Imaging and Vision, vol.21, issue.4, pp.210-230, 2012. ,
DOI : 10.1007/s10851-012-0392-5
Proximal splitting methods in signal processing In Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212, 2011. ,
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
Sparse solutions to linear inverse problems with multiple measurement vectors, IEEE Transactions on Signal Processing, vol.53, issue.7, pp.2477-2488, 2005. ,
DOI : 10.1109/TSP.2005.849172
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
Nonlinear Solution of Linear Inverse Problems by Wavelet???Vaguelette Decomposition, Applied and Computational Harmonic Analysis, vol.2, issue.2, pp.101-126, 1995. ,
DOI : 10.1006/acha.1995.1008
Uncertainty principles and ideal atomic decomposition Information Theory, IEEE Transactions on, vol.47, issue.143, pp.2845-2862, 2001. ,
DOI : 10.1109/18.959265
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.9300
Ideal spatial adaptation by wavelet shrinkage, Biometrika, vol.81, issue.3, pp.425-455, 1994. ,
DOI : 10.1093/biomet/81.3.425
A necessary and sufficient condition for exact sparse recovery by minimization, Comptes Rendus Mathematique, vol.350, issue.1-2, pp.117-120, 2012. ,
DOI : 10.1016/j.crma.2011.12.014
Sharp support recovery from noisy random measurements by <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi>???</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-minimization, Applied and Computational Harmonic Analysis, vol.33, issue.1, pp.24-43, 2012. ,
DOI : 10.1016/j.acha.2011.09.003
The degrees of freedom of the Lasso for general design matrix, Statistica Sinica, vol.23, issue.36, pp.809-828, 2013. ,
DOI : 10.5705/ss.2011.281
URL : https://hal.archives-ouvertes.fr/hal-00638417
On the Douglas???Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, vol.29, issue.1, pp.293-318, 1992. ,
DOI : 10.1007/BF01581204
How Biased is the Apparent Error Rate of a Prediction Rule?, Journal of the American Statistical Association, vol.39, issue.394, pp.461-470, 1986. ,
DOI : 10.1080/01621459.1986.10478291
Least angle regression, The Annals of statistics, vol.32, issue.2, pp.407-451, 2004. ,
Analysis versus synthesis in signal priors, Inverse Problems, vol.23, issue.3, p.947, 2007. ,
DOI : 10.1088/0266-5611/23/3/007
Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA), Applied and Computational Harmonic Analysis, vol.19, issue.3, pp.340-358, 2005. ,
DOI : 10.1016/j.acha.2005.03.005
URL : http://doi.org/10.1016/j.acha.2005.03.005
Generalized SURE for Exponential Families: Applications to Regularization, IEEE Transactions on Signal Processing, vol.57, issue.2, pp.471-481, 2009. ,
DOI : 10.1109/TSP.2008.2008212
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
On sparse representations in arbitrary redundant bases Information Theory, IEEE Transactions on, vol.50, issue.80, pp.1341-1344, 2004. ,
Linear convergence rates for Tikhonov regularization with positively homogeneous functionals, Inverse Problems, vol.27, issue.7, pp.75014-75040, 2011. ,
DOI : 10.1088/0266-5611/27/7/075014
Necessary and sufficient conditions for linear convergence of ???1-regularization, Communications on Pure and Applied Mathematics, vol.52, issue.3, pp.161-182, 2011. ,
DOI : 10.1002/cpa.20350
Should Penalized Least Squares Regression be Interpreted as Maximum A Posteriori Estimation?, IEEE Transactions on Signal Processing, vol.59, issue.5, pp.2405-2410, 2011. ,
DOI : 10.1109/TSP.2011.2107908
URL : https://hal.archives-ouvertes.fr/inria-00486840
Beyond sparsity: Recovering structured representations by ${\ell}^1$ minimization and greedy algorithms, Advances in Computational Mathematics, vol.49, issue.6, pp.23-41, 2008. ,
DOI : 10.1007/s10444-005-9009-5
URL : https://hal.archives-ouvertes.fr/inria-00544767
Atoms of All Channels, Unite! Average Case Analysis of??Multi-Channel Sparse Recovery Using Greedy Algorithms, Journal of Fourier Analysis and Applications, vol.86, issue.3, pp.5-6, 2008. ,
DOI : 10.1007/s00041-008-9044-y
URL : https://hal.archives-ouvertes.fr/inria-00146660
Recovering Low-Rank Matrices From Few Coefficients in Any Basis Information Theory, IEEE Transactions on, vol.57, issue.3, pp.1548-1566, 2011. ,
Sur lesprobì emes aux dérivées partielles et leur signification physique, Princeton University Bulletin, vol.13, pp.49-52, 1902. ,
Block threshold rules for curve estimation using kernel and wavelet methods, The Annals of Statistics, vol.26, issue.3, pp.922-942, 1998. ,
DOI : 10.1214/aos/1024691082
Numerical performance of block thresholded wavelet estimators, Statistics and Computing, vol.7, issue.2, pp.115-124, 1997. ,
DOI : 10.1023/A:1018569615247
Identifying Active Manifolds, Algorithmic Operations Research, vol.2, issue.227, p.114, 2007. ,
Convexifying the set of matrices of bounded rank: applications to the quasiconvexification and convexification of the rank function, Optimization Letters, vol.11, issue.5, pp.841-849, 2012. ,
DOI : 10.1007/s11590-011-0304-4
URL : https://hal.archives-ouvertes.fr/hal-00934783
A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators, Inverse Problems, vol.23, issue.3, pp.987-160, 2007. ,
DOI : 10.1088/0266-5611/23/3/009
Iterative image reconstruction from the bispectrum, Astronomy and Astrophysics, vol.278, pp.328-339, 1993. ,
A Natural Identity for Exponential Families with Applications in Multiparameter Estimation, The Annals of Statistics, vol.6, issue.3, pp.473-484, 1978. ,
DOI : 10.1214/aos/1176344194
Bayesian Methods in Nonlinear Digital Image Restoration, IEEE Transactions on Computers, vol.26, issue.3, pp.219-229, 1977. ,
DOI : 10.1109/TC.1977.1674810
Improving Upon Standard Estimators in Discrete Exponential Families with Applications to Poisson and Negative Binomial Cases, The Annals of Statistics, vol.10, issue.3, pp.857-867, 1982. ,
DOI : 10.1214/aos/1176345876
Improving Bag-of-Features for Large Scale Image Search, International Journal of Computer Vision, vol.42, issue.3, pp.316-336, 2010. ,
DOI : 10.1007/s11263-009-0285-2
Structured variable selection with sparsity-inducing norms, The Journal of Machine Learning Research, vol.12, pp.2777-2824, 2011. ,
URL : https://hal.archives-ouvertes.fr/inria-00377732
On the degrees of freedom in shrinkage estimation, Journal of Multivariate Analysis, vol.100, issue.7, pp.1338-1352, 2009. ,
DOI : 10.1016/j.jmva.2008.12.002
Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion, The Annals of Statistics, vol.39, issue.5, pp.2302-2329, 2011. ,
DOI : 10.1214/11-AOS894
URL : https://hal.archives-ouvertes.fr/hal-00676868
The Convex Analysis of Unitarily Invariant Matrix Functions, Journal of Convex Analysis, vol.2, issue.223, pp.173-183, 1995. ,
Alternating Projections on Manifolds, Mathematics of Operations Research, vol.33, issue.1, pp.216-234, 2008. ,
DOI : 10.1287/moor.1070.0291
URL : https://hal.archives-ouvertes.fr/hal-00317157
Partial Smoothness, Tilt Stability, and Generalized Hessians, SIAM Journal on Optimization, vol.23, issue.1, pp.74-94, 2013. ,
DOI : 10.1137/110852103
Splitting Algorithms for the Sum of Two Nonlinear Operators, SIAM Journal on Numerical Analysis, vol.16, issue.6, pp.964-979, 1979. ,
DOI : 10.1137/0716071
Image compression with edge-based inpainting Circuits and Systems for Video Technology, IEEE Transactions on, vol.17, issue.10, pp.1273-1287, 2007. ,
Convergence rates and source conditions for Tikhonov regularization with sparsity constraints, Journal of Inverse and Ill-posed Problems, vol.16, issue.5, pp.463-478, 2008. ,
DOI : 10.1515/JIIP.2008.025
Sparse MRI: The application of compressed sensing for rapid MR imaging, Magnetic Resonance in Medicine, vol.170, issue.6, pp.1182-1195, 2007. ,
DOI : 10.1002/mrm.21391
Uncertainty principles and vector quantization Information Theory, IEEE Transactions on, vol.56, issue.7, pp.3491-3501, 2010. ,
A theory for multiresolution signal decomposition: the wavelet representation Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.11, issue.20, pp.674-693, 1989. ,
Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3397-3415, 1993. ,
DOI : 10.1109/78.258082
Some Comments on C p, Technometrics, vol.15, issue.4, pp.661-675, 1973. ,
The group lasso for logistic regression, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.68, issue.1, pp.51-71, 2008. ,
DOI : 10.1111/j.1467-9868.2007.00627.x
On the degrees of freedom in shaperestricted regression, Annals of Statistics, vol.28, issue.4, pp.1083-1104, 2000. ,
Sensitivity analysis in nonsmooth optimization, Theoretical Aspects of Industrial Design, pp.32-46, 0199. ,
Proximité et dualité dans un espace hilbertien Bulletin de la Société mathématique de France 93, pp.273-299, 1965. ,
The cosparse analysis model and algorithms, Applied and Computational Harmonic Analysis, vol.34, issue.1, pp.30-56, 2013. ,
DOI : 10.1016/j.acha.2012.03.006
URL : https://hal.archives-ouvertes.fr/inria-00602205
Sparse Approximate Solutions to Linear Systems, SIAM Journal on Computing, vol.24, issue.2, pp.227-234, 1995. ,
DOI : 10.1137/S0097539792240406
Simultaneous support recovery in high dimensions: Benefits and perils of block-regularization Information Theory, IEEE Transactions on, vol.57, issue.6, pp.3841-3863, 2011. ,
Generalized Linear Models, Journal of the Royal Statistical Society. Series A (General), vol.135, issue.3, pp.370-384, 1972. ,
DOI : 10.2307/2344614
Certain Topics in Telegraph Transmission Theory, Transactions of the American Institute of Electrical Engineers, vol.47, issue.2, pp.617-644, 1928. ,
DOI : 10.1109/T-AIEE.1928.5055024
Joint covariate selection and joint subspace selection for multiple classification problems, Statistics and Computing, vol.8, issue.68, pp.231-252, 2010. ,
DOI : 10.1007/s11222-008-9111-x
A new approach to variable selection in least squares problems, IMA Journal of Numerical Analysis, vol.20, issue.3, pp.389-403, 2000. ,
DOI : 10.1093/imanum/20.3.389
Proximal Algorithms, Foundations and Trends?? in Optimization, vol.1, issue.3, pp.123-231, 2013. ,
DOI : 10.1561/2400000003
A SURE Approach for Digital Signal/Image Deconvolution Problems, IEEE Transactions on Signal Processing, vol.57, issue.12, pp.4616-4632, 2009. ,
DOI : 10.1109/TSP.2009.2026077
URL : https://hal.archives-ouvertes.fr/hal-00621942
A Generalized Forward-Backward Splitting, SIAM Journal on Imaging Sciences, vol.6, issue.3, pp.1199-1226, 2013. ,
DOI : 10.1137/120872802
URL : https://hal.archives-ouvertes.fr/hal-00613637
Monte-Carlo Sure: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms, IEEE Transactions on Image Processing, vol.17, issue.9, pp.1540-1554, 2008. ,
DOI : 10.1109/TIP.2008.2001404
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization, SIAM Review, vol.52, issue.3, pp.471-501, 2010. ,
DOI : 10.1137/070697835
Regularization of ill-posed problems in Banach spaces: convergence rates, Inverse Problems, vol.21, issue.4, pp.1303-1329, 2005. ,
DOI : 10.1088/0266-5611/21/4/007
On sparse reconstruction from Fourier and Gaussian measurements, Communications on Pure and Applied Mathematics, vol.52, issue.8, pp.1025-1045, 2008. ,
DOI : 10.1002/cpa.20227
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
Linear Inversion of Band-Limited Reflection Seismograms, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.4, pp.1307-1330, 1986. ,
DOI : 10.1137/0907087
Studies in the History of Probability and Statistics. XV The historical development of the Gauss linear model, Biometrika, vol.54, issue.12, pp.1-24, 1967. ,
A Mathematical Theory of Communication, Bell System Technical Journal, vol.27, issue.3, pp.379-423, 1948. ,
DOI : 10.1002/j.1538-7305.1948.tb01338.x
Adaptive Model Selection, Journal of the American Statistical Association, vol.97, issue.457, pp.210-221, 2002. ,
DOI : 10.1198/016214502753479356
Deconvolution in Astronomy: A Review, Publications of the Astronomical Society of the Pacific, vol.114, issue.800, pp.1051-1069, 2002. ,
DOI : 10.1086/342606
On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and SIDEs, SIAM Journal on Numerical Analysis, vol.42, issue.2, pp.686-713, 2004. ,
DOI : 10.1137/S0036142903422429
Estimation of the Mean of a Multivariate Normal Distribution, The Annals of Statistics, vol.9, issue.6, pp.1135-1151, 1981. ,
DOI : 10.1214/aos/1176345632
Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical Society. Series B. Methodological, vol.58, issue.1, pp.267-288, 1996. ,
The solution path of the generalized lasso, The Annals of Statistics, vol.39, issue.3, pp.1335-1371, 2011. ,
DOI : 10.1214/11-AOS878SUPP
Sparsity and smoothness via the fused lasso, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.99, issue.1, pp.91-108, 2005. ,
DOI : 10.1016/S0140-6736(02)07746-2
Just relax: Convex programming methods for identifying sparse signals in noise Information Theory, IEEE Transactions on, vol.52, issue.180, pp.1030-1051, 2006. ,
Innovation Rate Sampling of Pulse Streams With Application to Ultrasound Imaging, IEEE Transactions on Signal Processing, vol.59, issue.4, pp.1827-1842, 2011. ,
DOI : 10.1109/TSP.2011.2105480
Simultaneous Variable Selection, Technometrics, vol.47, issue.3, pp.349-363, 2005. ,
DOI : 10.1198/004017005000000139
Local behavior of sparse analysis regularization: Applications to risk estimation, Applied and Computational Harmonic Analysis, vol.35, issue.3, pp.433-451, 2013. ,
DOI : 10.1016/j.acha.2012.11.006
URL : https://hal.archives-ouvertes.fr/hal-00687751
Robust Sparse Analysis Regularization, IEEE Transactions on Information Theory, vol.59, issue.4, pp.2001-2016, 2013. ,
DOI : 10.1109/TIT.2012.2233859
URL : https://hal.archives-ouvertes.fr/hal-00627452
High-dimensional generalized linear models and the lasso, The Annals of Statistics, vol.36, issue.2, pp.614-645, 2008. ,
DOI : 10.1214/009053607000000929
Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using <formula formulatype="inline"><tex Notation="TeX">$\ell _{1}$</tex> </formula>-Constrained Quadratic Programming (Lasso), IEEE Transactions on Information Theory, vol.55, issue.5, pp.2183-2202, 2009. ,
DOI : 10.1109/TIT.2009.2016018
Characterization of the subdifferential of some matrix norms, Linear Algebra and its Applications, vol.170, pp.33-45, 1992. ,
DOI : 10.1016/0024-3795(92)90407-2
Identifiable Surfaces in Constrained Optimization, SIAM Journal on Control and Optimization, vol.31, issue.4, pp.1063-1079, 1993. ,
DOI : 10.1137/0331048
On Measuring and Correcting the Effects of Data Mining and Model Selection, Journal of the American Statistical Association, vol.87, issue.441, pp.120-131, 1998. ,
DOI : 10.1080/01621459.1998.10474094
Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.58, issue.1, pp.49-67, 2005. ,
DOI : 10.1198/016214502753479356
The composite absolute penalties family for grouped and hierarchical variable selection, The Annals of Statistics, vol.37, issue.6A, pp.3468-3497, 2009. ,
DOI : 10.1214/07-AOS584
Regularization and variable selection via the elastic net, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.5, issue.2, pp.301-320, 2005. ,
DOI : 10.1073/pnas.201162998
On the ???degrees of freedom??? of the lasso, The Annals of Statistics, vol.35, issue.5, pp.2173-2192, 2007. ,
DOI : 10.1214/009053607000000127
Information theory and an extension of the maximum likelihood principle, Second international symposium on information theory, pp.267-281, 1973. ,
A rank minimization heuristic with application to minimum order system approximation, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), pp.4734-4739, 2001. ,
DOI : 10.1109/ACC.2001.945730
Spread representations, 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), pp.814-817, 2011. ,
DOI : 10.1109/ACSSC.2011.6190120
URL : https://hal.archives-ouvertes.fr/hal-00700734
Anti-sparse coding for approximate nearest neighbor search, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.2029-2032, 2012. ,
DOI : 10.1109/ICASSP.2012.6288307
Learning exponential families in high-dimensions: Strong convexity and sparsity, JMLR Workshop and Conference Proceedings, pp.381-388, 2010. ,
Estimation Consistency of the Group Lasso and its Applications, Proceedings of the 12th International Conference on Artificial Intelligence and Statistics (AISTATS), 2009. ,
Greedy signal recovery review, 2008 42nd Asilomar Conference on Signals, Systems and Computers, pp.1048-1050, 2008. ,
DOI : 10.1109/ACSSC.2008.5074572
URL : http://arxiv.org/abs/0812.2202
A Unified Framework for High-Dimensional Analysis of $M$-Estimators with Decomposable Regularizers, Proc. NIPS, pp.1348-1356, 2009. ,
DOI : 10.1214/12-STS400SUPP
Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, pp.40-44, 1993. ,
DOI : 10.1109/ACSSC.1993.342465
Adaptive Structured Block Sparsity Via Dyadic Partitioning, Proc. EUSIPCO 2011, pp.1455-1459, 2011. ,
Inpainting the colors, IEEE International Conference on Image Processing 2005, pp.698-705, 2005. ,
DOI : 10.1109/ICIP.2005.1530151
Signal restoration with overcomplete wavelet transforms: comparison of analysis and synthesis priors, Wavelets XIII, pp.74460-74476, 2009. ,
DOI : 10.1117/12.826663
A SURE-fired way to choose smoothing parameters in illconditioned inverse problems, IEEE Int. Conf. Image Process. (ICIP), pp.89-92, 1996. ,
Threshold selection for group sparsity, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.3754-3757, 2010. ,
DOI : 10.1109/ICASSP.2010.5495858
Signal Representations with Minimum ? ? -Norm, Communication, Control, and Computing, Proc. 50th Ann. Allerton Conf. on, 2012. ,
Compressive sensing off the grid, 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp.778-785, 2012. ,
DOI : 10.1109/Allerton.2012.6483297
A Complete Analysis of the l 1,p Group-Lasso, Machine Learning, International Conference on, p.18, 2012. ,
Recursive risk estimation for non-linear image deconvolution with a wavelet-domain sparsity constraint, 2008 15th IEEE International Conference on Image Processing, pp.665-668, 2008. ,
DOI : 10.1109/ICIP.2008.4711842
An Architecture for Compressive Imaging, 2006 International Conference on Image Processing, pp.1273-1276, 2006. ,
DOI : 10.1109/ICIP.2006.312577
Adaptive regression and model selection in data mining problems, PhD diss., Australian National University, 1999. ,
Curvelets: A surprisingly effective nonadaptive representation for objects with edges, p.14, 2000. ,
An Introduction to O-minimal Geometry Lecture notes, pp.69-71, 1999. ,
Orthogonal Invariance and Identifiability, SIAM Journal on Matrix Analysis and Applications, vol.35, issue.2, p.114, 2013. ,
DOI : 10.1137/130916710
URL : http://arxiv.org/abs/1304.1198
Adaptive Time-Frequency Approximations with Matching Pursuits, Courant Institute of Mathematical Sciences, 1994. ,
DOI : 10.1016/B978-0-08-052084-1.50018-1
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.2830
Stein Unbiased GrAdient estimator of the Risk (SUGAR) for Multiple Parameter Selection, SIAM Journal on Imaging Sciences, vol.7, issue.4, p.243, 2014. ,
DOI : 10.1137/140968045
URL : https://hal.archives-ouvertes.fr/hal-00987295
Exact Support Recovery for Sparse Spikes Deconvolution, Foundations of Computational Mathematics, vol.15, issue.5, pp.138-179, 2013. ,
DOI : 10.1007/s10208-014-9228-6
URL : https://hal.archives-ouvertes.fr/hal-00839635
Matrix Rank Minimization with Applications PhD diss, p.18, 2002. ,
Theory of Ill-Posed Linear Problems and Its Applications, 1978. ,
DOI : 10.1515/9783110944822
Learning with matrix factorizations, 2004. ,