L. , L. Magoarou, and R. Gribonval, Learning computationally efficient dictionaries and their implementation as fast transforms, 1406.
URL : https://hal.archives-ouvertes.fr/hal-01010577

L. Magoarou and R. Gribonval, Chasing butterflies: In search of efficient dictionaries, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2015.
DOI : 10.1109/ICASSP.2015.7178579

URL : https://hal.archives-ouvertes.fr/hal-01104696

J. Cooley and J. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, vol.19, issue.90, pp.297-301, 1965.
DOI : 10.1090/S0025-5718-1965-0178586-1

J. Shanks, Computation of the Fast Walsh-Fourier Transform, IEEE Transactions on Computers, vol.18, issue.5, pp.457-459, 1969.
DOI : 10.1109/T-C.1969.222685

W. Chen, C. Smith, and S. Fralick, A Fast Computational Algorithm for the Discrete Cosine Transform, IEEE Transactions on Communications, vol.25, issue.9, pp.1004-1009, 1977.
DOI : 10.1109/TCOM.1977.1093941

S. Mallat, A theory for multiresolution signal decomposition: the wavelet representation Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.11, issue.7, pp.674-693, 1989.

J. Morgenstern, The Linear Complexity of Computation, Journal of the ACM, vol.22, issue.2, pp.184-194, 1975.
DOI : 10.1145/321879.321881

S. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3397-3415, 1993.
DOI : 10.1109/78.258082

I. Daubechies, M. Defrise, and C. Mol, 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

J. Tropp and A. Gilbert, Signal recovery from random measurements via orthogonal matching pursuit Information Theory, IEEE Transactions on, vol.53, issue.12, pp.4655-4666, 2007.

T. Blumensath and M. E. Davies, Iterative Thresholding for Sparse Approximations, Journal of Fourier Analysis and Applications, vol.73, issue.10, pp.629-654, 2008.
DOI : 10.1007/s00041-008-9035-z

A. Beck and M. Teboulle, 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

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.3271

R. Rubinstein, A. Bruckstein, and M. Elad, Dictionaries for Sparse Representation Modeling, Proceedings of the IEEE, pp.1045-1057, 2010.
DOI : 10.1109/JPROC.2010.2040551

URL : https://hal.archives-ouvertes.fr/inria-00565811

R. Rubinstein, M. Zibulevsky, and M. Elad, Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation, IEEE Transactions on Signal Processing, vol.58, issue.3, pp.1553-1564, 2010.
DOI : 10.1109/TSP.2009.2036477

O. Chabiron, F. Malgouyres, J. Tourneret, and N. Dobigeon, Toward Fast Transform Learning, International Journal of Computer Vision, vol.60, issue.12, pp.195-216, 2015.
DOI : 10.1007/s11263-014-0771-z

URL : https://hal.archives-ouvertes.fr/hal-00862903

D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega, and P. Vandergheynst, The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains, IEEE Signal Processing Magazine, vol.30, issue.3, pp.83-98, 2013.
DOI : 10.1109/MSP.2012.2235192

L. , L. Magoarou, R. Gribonval, and A. Gramfort, FAµST: speeding up linear transforms for tractable inverse problems, EUSIPCO, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01156478

J. Bolte, S. Sabach, and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Mathematical Programming, pp.1-36, 2013.
DOI : 10.1007/s10107-013-0701-9

URL : https://hal.archives-ouvertes.fr/hal-00916090

E. Jones, T. Oliphant, and P. Peterson, SciPy: Open source scientific tools for Python, 2001.

R. Gribonval, R. Jenatton, F. Bach, M. Kleinsteuber, and M. Seibert, Sample complexity of dictionary learning and other matrix factorizations Information Theory, IEEE Transactions on, vol.61, issue.6, pp.3469-3486, 2015.

V. Rokhlin, Rapid solution of integral equations of classical potential theory, Journal of Computational Physics, vol.60, issue.2, pp.187-207, 1985.
DOI : 10.1016/0021-9991(85)90002-6

W. Hackbusch, A Sparse Matrix Arithmetic Based on $\Cal H$ -Matrices. Part I: Introduction to ${\Cal H}$ -Matrices, Computing, vol.62, issue.2, pp.89-108, 1999.
DOI : 10.1007/s006070050015

E. Candès, L. Demanet, and L. Ying, Fast Computation of Fourier Integral Operators, SIAM Journal on Scientific Computing, vol.29, issue.6, pp.2464-2493, 2007.
DOI : 10.1137/060671139

G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Communications on Pure and Applied Mathematics, vol.1, issue.2, pp.141-183, 1991.
DOI : 10.1002/cpa.3160440202

I. Tosic and P. Frossard, Dictionary Learning, IEEE Signal Processing Magazine, vol.28, issue.2, pp.27-38, 2011.
DOI : 10.1109/MSP.2010.939537

A. M. Bruckstein, D. L. Donoho, and M. Elad, From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images, SIAM Review, vol.51, issue.1, pp.34-81, 2009.
DOI : 10.1137/060657704

K. Gregor and Y. Lecun, Learning fast approximations of sparse coding, Proceedings of the 27th Annual International Conference on Machine Learning, ser. ICML '10, pp.399-406, 2010.

P. Sprechmann, A. M. Bronstein, and G. Sapiro, Learning efficient sparse and low rank models Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.37, issue.9, pp.1821-1833, 2015.

A. Makhzani and B. Frey, k-sparse autoencoders, 1312.

A. B. Lee, B. Nadler, and L. Wasserman, Treelets???An adaptive multi-scale basis for sparse unordered data, The Annals of Applied Statistics, vol.2, issue.2, pp.435-471, 2008.
DOI : 10.1214/07-AOAS137

G. Cao, L. Bachega, and C. Bouman, The Sparse Matrix Transform for Covariance Estimation and Analysis of High Dimensional Signals, IEEE Transactions on Image Processing, vol.20, issue.3, pp.625-640, 2011.
DOI : 10.1109/TIP.2010.2071390

S. Lyu and X. Wang, On algorithms for sparse multi-factor NMF, Advances in Neural Information Processing Systems, pp.602-610, 2013.

B. Neyshabur and R. Panigrahy, Sparse matrix factorization, 1311.

S. Arora, A. Bhaskara, R. Ge, and T. Ma, Provable bounds for learning some deep representations, 1310.

V. G. Kondor and N. Teneva, Multiresolution matrix factorization, pp.1620-1628, 2014.

R. Rustamov and L. Guibas, Wavelets on graphs via deep learning, Advances in Neural Information Processing Systems 26, pp.998-1006, 2013.

Y. Bengio, P. Lamblin, D. Popovici, and H. Larochelle, Greedy layerwise training of deep networks Advances in neural information processing systems, p.153, 2007.

Y. Bengio, Learning Deep Architectures for AI, Foundations and Trends?? in Machine Learning, vol.2, issue.1, pp.1-127, 2009.
DOI : 10.1561/2200000006

G. E. Hinton and R. R. Salakhutdinov, Reducing the Dimensionality of Data with Neural Networks, Science, vol.313, issue.5786, pp.504-507, 2006.
DOI : 10.1126/science.1127647

S. Haufe, V. V. Nikulin, A. Ziehe, K. Müller, and G. Nolte, Combining sparsity and rotational invariance in EEG/MEG source reconstruction, NeuroImage, vol.42, issue.2, pp.726-738, 2008.
DOI : 10.1016/j.neuroimage.2008.04.246

A. Gramfort, M. Kowalski, and M. S. Hämäläinen, Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods, Physics in Medicine and Biology, vol.57, issue.7, pp.1937-1961, 2012.
DOI : 10.1088/0031-9155/57/7/1937

URL : https://hal.archives-ouvertes.fr/hal-00690774

A. Gramfort, M. Luessi, E. Larson, D. A. Engemann, D. Strohmeier et al., MNE software for processing MEG and EEG data, NeuroImage, vol.86, issue.0, pp.446-460, 2014.
DOI : 10.1016/j.neuroimage.2013.10.027

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3930851

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, An interiorpoint method for large-scale l1-regularized least squares Selected Topics in Signal Processing, IEEE Journal, vol.1, issue.4, pp.606-617, 2007.

]. K. Engan, S. Aase, and J. H. Husoy, Method of optimal directions for frame design, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258), pp.2443-2446, 1999.
DOI : 10.1109/ICASSP.1999.760624

M. Aharon, M. Elad, and A. Bruckstein, <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

J. Mairal, F. Bach, J. Ponce, and G. Sapiro, Online learning for matrix factorization and sparse coding, Journal of Machine Learning Research, vol.11, issue.1, pp.19-60, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00408716

R. Rubinstein, M. Zibulevsky, and M. Elad, Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit, 2008.

M. Elad and M. Aharon, Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries, IEEE Transactions on Image Processing, vol.15, issue.12, pp.3736-3745, 2006.
DOI : 10.1109/TIP.2006.881969

D. Vainsencher, S. Mannor, and A. M. Bruckstein, The sample complexity of dictionary learning, The Journal of Machine Learning Research, vol.12, pp.3259-3281, 2011.

A. Maurer and M. Pontil, K-Dimensional Coding Schemes in Hilbert Spaces Information Theory, IEEE Transactions on, vol.56, issue.11, pp.5839-5846, 2010.