Skip to article frontmatterSkip to article content
Site not loading correctly?

This may be due to an incorrect BASE_URL configuration. See the MyST Documentation for reference.

References

CNRS & DMA, École Normale Supérieure

[1] Andrew R Barron. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information theory, 39(3):930–945, 1993.

[2] Amir Beck. Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with MATLAB. SIAM, 2014.

[3] Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends® in Machine Learning, 3(1):1–122, 2011.

[4] Stephen Boyd and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.

[5] E. Candès and D. Donoho. New tight frames of curvelets and optimal representations of objects with piecewise C2\text{C}^2 singularities. Commun. on Pure and Appl. Math., 57(2):219–266, 2004.

[6] E. J. Candès. The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathématique, 346(9–10):589–592, 2008.

[7] E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying. Fast discrete curvelet transforms. SIAM Multiscale Modeling and Simulation, 5:861–899, 2005.

[8] Emmanuel J. Candès and Terence Tao. Decoding by linear programming. IEEE Transactions on Information Theory, 51(12):4203–4215, 2005.

[9] A. Chambolle. An algorithm for total variation minimization and applications. J. Math. Imaging Vis., 20:89–97, 2004.

[10] Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga, and Thomas Pock. An introduction to total variation for image analysis. Theoretical foundations and numerical methods for sparse recovery, 9(263-340):227, 2010.

[11] Antonin Chambolle and Thomas Pock. An introduction to continuous optimization for imaging. Acta Numerica, 25:161–319, 2016.

[12] S.S. Chen, D.L. Donoho, and M.A. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20(1):33–61, 1999.

[13] Philippe G Ciarlet. Introduction à l’analyse numérique matricielle et à l’optimisation. Masson, 1982.

[14] P. L. Combettes and V. R. Wajs. Signal recovery by proximal forward-backward splitting. SIAM Multiscale Modeling and Simulation, 4(4), 2005.

[15] George Cybenko. Approximation by superpositions of a sigmoidal function. Mathematics of control, signals and systems, 2(4):303–314, 1989.

[16] I. Daubechies, M. Defrise, and C. De Mol. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. on Pure and Appl. Math., 57:1413–1541, 2004.

[17] D. Donoho and I. Johnstone. Ideal spatial adaptation via wavelet shrinkage. Biometrika, 81:425–455, Dec 1994.

[18] Marco F. Duarte, Mark A. Davenport, Dharmpal Takhar, Jason N. Laska, Ting Sun, Kevin F. Kelly, and Richard G. Baraniuk. Single-pixel imaging via compressive sampling. IEEE Signal Processing Magazine, 25(2):83–91, 2008.

[19] Heinz Werner Engl, Martin Hanke, and Andreas Neubauer. Regularization of inverse problems, volume 375. Springer Science & Business Media, 1996.

[20] M. Figueiredo and R. Nowak. An EM Algorithm for Wavelet-Based Image Restoration. IEEE Trans. Image Proc., 12(8):906–916, 2003.

[21] Simon Foucart and Holger Rauhut. A mathematical introduction to compressive sensing. Birkhäuser Basel, 2013.

[22] Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In Proceedings of the 32nd International Conference on Machine Learning, volume 37, pages 448–456. PMLR, 2015.

[23] Stephane Mallat. A wavelet tour of signal processing: the sparse way. Academic press, 2008.

[24] D. Mumford and J. Shah. Optimal approximation by piecewise smooth functions and associated variational problems. Commun. on Pure and Appl. Math., 42:577–685, 1989.

[25] Neal Parikh, Stephen Boyd, et al. Proximal algorithms. Foundations and Trends® in Optimization, 1(3):127–239, 2014.

[26] Gabriel Peyré. L’algèbre discrète de la transformée de Fourier. Ellipses, 2004.

[27] J. Portilla, V. Strela, M.J. Wainwright, and Simoncelli E.P. Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. Image Proc., 12(11):1338–1351, November 2003.

[28] L. I. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. Phys. D, 60(1-4):259–268, 1992.

[29] Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen, and L Sirovich. Variational methods in imaging. Springer, 2009.

[30] C. E. Shannon. A mathematical theory of communication. The Bell System Technical Journal, 27(3):379–423, 1948.

[31] Jean-Luc Starck, Fionn Murtagh, and Jalal Fadili. Sparse image and signal processing: Wavelets and related geometric multiscale analysis. Cambridge university press, 2015.

[32] Joel A. Tropp. Just relax: Convex programming methods for identifying sparse signals in noise. IEEE Transactions on Information Theory, 52(3):1030–1051, 2006.

[33] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in Neural Information Processing Systems, volume 30, 2017.