, 1) holds because x is k-sparse and b |k is the best k-sparse approximation of b |R since supp(b |k ) = supp(x t+1 ) ? R, p.1
Generalized sampling and infinite-dimensional compressed sensing, Foundations of Computational Mathematics, vol.16, issue.5, pp.1263-1323, 2016. ,
Greedy sparsity-constrained optimization, J. of Machine Learning Research, vol.14, issue.3, pp.807-841, 2013. ,
The asymptotic behavior of the composition of two resolvents, Nonlinear Analysis: Theory, Methods, and Applications, vol.5, pp.283-301, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00017826
The baillon-haddad theorem revisited, J. of Convex Analysis, vol.17, issue.4, pp.781-787, 2010. ,
Convex analysis and monotone operator theory in Hilbert spaces, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00643354
On the minimization over sparse symmetric sets: Projections, optimality conditions, and algorithms, 2015. ,
Compressed sensing with nonlinear observations and related nonlinear optimization problems, IEEE Transactions on Information Theory, vol.59, issue.6, pp.3466-3474, 2013. ,
Patch-based nonlocal functional for denoising fluorescence microscopy image sequences, IEEE Trans. Med. Imaging, vol.29, issue.2, pp.442-454, 2008. ,
Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. Information Theory, IEEE Trans. on, vol.52, issue.2, pp.489-509, 2006. ,
Iterative methods for fixed point problems in Hilbert spaces, 2013. ,
Epigraphical projection and proximal tools for solving constrained convex optimization problems: Part i, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00744603
A Douglas-Rachford splittting approach to nonsmooth convex variational signal recovery, IEEE J. Selec. Top. Sig. Pro, vol.1, issue.4, pp.564-574, 2007. ,
Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Set-Valued and variational analysis, vol.20, pp.307-330, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00794044
Subspace pursuit for compressive sensing signal reconstruction, IEEE Transactions on Information Theory, vol.55, issue.5, pp.2230-2249, 2009. ,
Hard thresholding pursuit: an algorithm for compressive sensing, SIAM Journal on Numerical Analysis, vol.49, issue.6, pp.2543-2563, 2011. ,
Orthogonal matching pursuit with replacement, Advances in Neural Information Processing Systems 24, pp.1215-1223, 2011. ,
On iterative hard thresholding methods for high-dimensional m-estimation, Advances in Neural Information Processing Systems, pp.685-693, 2014. ,
On learning discrete graphical models using greedy methods, Advances in Neural Information Processing Systems 24, pp.1935-1943, 2011. ,
Continuous compressed sensing for surface dynamical processes with helium atom scattering, Scientific reports, vol.6, p.27776, 2016. ,
Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis, vol.48, 2011. ,
Practical Aspects of the Moreau-Yosida Regularization: Theoretical Preliminaries, SIAM J. on Optimization, vol.7, issue.2, pp.367-385, 1997. ,
Optimal inversion of the anscombe transformation in low-count poisson image denoising. Image Processing, IEEE Trans. on, vol.20, issue.1, pp.99-109, 2011. ,
Matching pursuits with time-frequency dictionaries. Signal Processing, IEEE Trans. on, vol.41, issue.12, pp.3397-3415, 1993. ,
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples, Applied and Computational Harmonic Analysis, vol.26, issue.3, pp.301-321, 2009. ,
Group sparsity with overlapping partition functions, Signal Processing Conference, pp.303-307, 2011. ,
Trading accuracy for sparsity in optimization problems with sparsity constraints, SIAM Journal on Optimization, vol.20, issue.6, pp.2807-2832, 2010. ,
Greedy approximation, Acta Numerica, vol.17, pp.235-409, 2008. ,
Greed is good: Algorithmic results for sparse approximation, IEEE Trans. Inf. Theor, vol.50, issue.10, pp.2231-2242, 2006. ,
Local behavior of sparse analysis regularization: Applications to risk estimation, Applied and Computational Harmonic Analysis, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00687751
Image quality assessment: From error visibility to structural similarity. Image Processing, IEEE Trans. on, vol.13, issue.4, 2004. ,
Sparse nonlinear regression: Parameter estimation under nonconvexity, Proceedings of the 33nd International Conference on Machine Learning, pp.2472-2481, 2016. ,
Gradient hard thresholding pursuit for sparsity-constrained optimization, The 31st International Conference on Machine Learning, pp.127-135, 2014. ,
Wavelets, ridgelets, and curvelets for Poisson noise removal. Image Processing, IEEE Trans. on, vol.17, issue.7, pp.1093-1108, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00259509
Sparse recovery with orthogonal matching pursuit under RIP. Information Theory, IEEE Trans. on, vol.57, issue.9, pp.6215-6221, 2011. ,