J. Bobin, F. Sureau, J. Starck, A. Rassat, and P. Paykari, Joint Planck and WMAP CMB map reconstruction, Astronomy and Astrophysics -A&A, vol.563, 201322372.
DOI : 10.1051/0004-6361/201322372

URL : https://hal.archives-ouvertes.fr/cea-01234362

J. Bobin, J. Rapin, A. Larue, and J. L. Starck, Sparsity and Adaptivity for the Blind Separation of Partially Correlated Sources, IEEE Transactions on Signal Processing, vol.63, issue.5, pp.1199-1213, 2015.
DOI : 10.1109/TSP.2015.2391071

URL : https://hal.archives-ouvertes.fr/hal-01093148

J. Bobin, J. Starck, J. Fadili, and Y. Moudden, Sparsity and Morphological Diversity in Blind Source Separation, IEEE Transactions on Image Processing, vol.16, issue.11, pp.2662-2674, 2007.
DOI : 10.1109/TIP.2007.906256

URL : https://hal.archives-ouvertes.fr/hal-01125600

J. Bobin, J. Starck, and R. Ottensamer, Compressed Sensing in Astronomy, IEEE Journal of Selected Topics in Signal Processing, vol.2, issue.5, pp.718-726, 2008.
DOI : 10.1109/JSTSP.2008.2005337

J. Bolte, S. Sabach, and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Mathematical Programming, pp.459-494, 2014.
DOI : 10.1007/BF01584660

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

F. L. Boone, interférométrie comme technique d'imagerie: principe et instrumentation, pp.113-150, 2011.

S. Boyd and L. Vandenberghe, Convex optimization, p.64, 2004.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Machine Learning, pp.1-122, 2011.
DOI : 10.1561/2200000016

N. Bracewell and G. W. Preston, Radio Reflection and Refraction Phenomena in the High Solar Corona., The Astrophysical Journal, vol.123, pp.14-78, 1956.
DOI : 10.1086/146125

R. N. Bracewell and J. A. Roberts, Aerial Smoothing in Radio Astronomy, Australian Journal of Physics, vol.7, issue.4, p.615, 1954.
DOI : 10.1071/PH540615

URL : http://www.publish.csiro.au/ph/pdf/ph540615

D. S. Briggs, High Fidelity Deconvolution of Moderately Resolved Sources. D. Briggs, 1995. URL https

J. Cai, E. J. Candès, and Z. Shen, A Singular Value Thresholding Algorithm for Matrix Completion, SIAM Journal on Optimization, vol.20, issue.4, pp.1956-1982, 2010.
DOI : 10.1137/080738970

URL : http://arxiv.org/pdf/0810.3286

E. Candes and J. Romberg, Sparsity and incoherence in compressive sampling Inverse problems, pp.969-83, 2007.

J. Emmanuel, T. Candes, and . Tao, Decoding by linear programming, IEEE transactions on information theory, vol.51, issue.55, pp.4203-4215, 2005.

J. Emmanuel, T. Candes, and . Tao, Near-optimal signal recovery from random projections: Universal encoding strategies?, IEEE transactions on information theory, vol.52, issue.12, pp.5406-5425, 2006.

J. Emmanuel, . Candès, B. Michael, and . Wakin, An introduction to compressive sampling, IEEE signal processing magazine, vol.25, issue.2, pp.21-30, 2008.

J. Emmanuel, J. Candès, T. Romberg, and . Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on information theory, vol.52, issue.55, pp.489-509, 2006.

J. Emmanuel, . Candes, K. Justin, T. Romberg, and . Tao, Stable signal recovery from incomplete and inaccurate measurements, Communications on pure and applied mathematics, vol.59, issue.8, pp.1207-1223, 2006.

J. Emmanuel, . Candes, B. Michael, . Wakin, P. Stephen et al., Enhancing sparsity by reweighted 1 minimization, Journal of Fourier analysis and applications, vol.14, issue.5, pp.877-905, 2008.

J. Stappers, R. Van-leeuwen, P. Wijnands, and . Zarka, New methods to constrain the radio transient rate: results from a survey of four fields with LOFAR. ArXiv e-prints, p.77, 2014.
URL : https://hal.archives-ouvertes.fr/insu-01338196

E. Rafael, . Carrillo, Y. Mcewen, and . Wiaux, Sparsity averaging reweighted analysis (sara): a novel algorithm for radio-interferometric imaging, Monthly Notices of the Royal Astronomical Society, vol.426, issue.2, pp.1223-1234, 2012.

E. Rafael, J. D. Carrillo, Y. Mcewen, and . Wiaux, Purify: a new approach to radio-interferometric imaging, Monthly Notices of the Royal Astronomical Society, vol.439, issue.60, pp.3591-3604, 2014.

S. Law, M. Markoff, B. Pietka, M. Stappers, P. Wise et al., LOFAR Observations of Swift J1644+57 and Implications for Short-Duration Transients. ArXiv e-prints, p.77, 2014.

A. Chambolle and T. Pock, 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 : 10.1007/978-3-540-74936-3_22

URL : https://hal.archives-ouvertes.fr/hal-00490826

E. Chapman, A. Bonaldi, G. Harker, V. Jeli?, F. B. Abdalla et al., Cosmic dawn and epoch of reionization foreground removal with the ska. arXiv preprint, p.54, 2015.

N. Jayaram and . Chengalur, Two element interferometers URL http://gmrt. ncra.tifr.res.in/gmrt_hpage, p.13, 2003.

E. Chouzenoux, J. Pesquet, and A. Repetti, A block coordinate variable metric forward???backward algorithm, Journal of Global Optimization, vol.6, issue.3, pp.1-29, 2016.
DOI : 10.1137/120887795

URL : https://hal.archives-ouvertes.fr/hal-00945918

B. G. Clark, An efficient implementation of the algorithm, A&A, vol.89, p.377, 1926.

B. Butcher, A. Ciardi, A. Corstanje, S. Deller, J. Duscha et al., The LOFAR pilot surveys for pulsars and fast radio transients, A&A, vol.570, pp.60-77, 2014.
URL : https://hal.archives-ouvertes.fr/insu-01277801

A. Cohen, I. Daubechies, and J. Feauveau, Biorthogonal bases of compactly supported wavelets, Communications on Pure and Applied Mathematics, vol.10, issue.5, pp.485-560, 1992.
DOI : 10.1002/cpa.3160450502

L. Patrick, J. Combettes, and . Pesquet, Proximal splitting methods in signal processing In Fixed-point algorithms for inverse problems in science and engineering, pp.185-212, 2011.

L. Patrick, V. R. Combettes, and . Wajs, Signal recovery by proximal forwardbackward splitting, Multiscale Modeling & Simulation, vol.4, issue.67, pp.1168-1200, 2005.

L. Condat, 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, 2013.
DOI : 10.1081/NFA-120003674

URL : https://hal.archives-ouvertes.fr/hal-00609728

J. Cornwell, Multiscale CLEAN Deconvolution of Radio Synthesis Images, IEEE Journal of Selected Topics in Signal Processing, vol.2, issue.5, pp.793-801, 2008.
DOI : 10.1109/JSTSP.2008.2006388

URL : http://arxiv.org/pdf/0806.2228

J. Cornwell and K. F. Evans, A simple maximum entropy deconvolution algorithm, A&A, vol.143, pp.77-83, 1926.

T. J. Cornwell, K. Golap, and S. Bhatnagar, The Noncoplanar Baselines Effect in Radio Interferometry: The W-Projection Algorithm, IEEE Journal of Selected Topics in Signal Processing, vol.2, issue.5, pp.647-657, 2008.
DOI : 10.1109/JSTSP.2008.2005290

A. Dabbech, C. Ferrari, D. Mary, E. Slezak, O. Smirnov et al., MORESANE: MOdel REconstruction by Synthesis-ANalysis Estimators, Astronomy & Astrophysics, vol.400
DOI : 10.1111/j.1365-2966.2009.15519.x

URL : http://www.aanda.org/articles/aa/pdf/2015/04/aa24602-14.pdf

J. Deguignet, A. Ferrari, D. Mary, and C. Ferrari, Distributed multi-frequency image reconstruction for radio-interferometry, 2016 24th European Signal Processing Conference (EUSIPCO), pp.1483-1487, 2016.
DOI : 10.1109/EUSIPCO.2016.7760495

URL : http://arxiv.org/pdf/1602.08847

J. W. Kondratiev, F. A. Hessels, L. Jenet, V. M. Kasian, M. Kaspi et al., Arecibo Pulsar Survey Using ALFA: Probing Radio Pulsar Intermittency And Transients, ApJ, vol.703, issue.2, pp.2259-2274, 2009.

P. E. Dewdney, P. J. Hall, R. T. Schilizzi, and T. J. Lazio, The Square Kilometre Array, Proceedings of the IEEE, vol.97, issue.8, pp.1482-1496, 2009.
DOI : 10.1109/JPROC.2009.2021005

L. David and . Donoho, Compressed sensing, IEEE Transactions on information theory, vol.52, issue.55, pp.1289-1306, 1932.

L. David and . Donoho, For most large underdetermined systems of linear equations the minimal 1 -norm solution is also the sparsest solution, Communications on pure and applied mathematics, vol.59, issue.6, pp.797-829, 2006.

L. David, X. Donoho, and . Huo, Uncertainty principles and ideal atomic decomposition, IEEE Transactions on Information Theory, vol.47, issue.7, pp.2845-2862, 2001.

L. David, . Donoho, M. Jain, and . Johnstone, Ideal spatial adaptation by wavelet shrinkage, biometrika, vol.81, issue.3, pp.425-455, 1994.

S. C. Douglas, H. Sawada, and S. Makino, Natural gradient multichannel blind deconvolution and speech separation using causal FIR filters, IEEE Transactions on Speech and Audio Processing, vol.13, issue.1, pp.92-104, 2005.
DOI : 10.1109/TSA.2004.838538

K. S. Dwarakanath, What would the sky look like at long radio wavelengths?
DOI : 10.1093/mnras/279.1.257

M. Elad, J. Starck, P. Querre, L. David, and . Donoho, 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 : https://doi.org/10.1016/j.acha.2005.03.005

M. Elad, P. Milanfar, and R. Rubinstein, Analysis versus synthesis in signal priors, Inverse Problems, vol.23, issue.3, pp.947-59, 2007.
DOI : 10.1088/0266-5611/23/3/007

URL : http://www.cs.technion.ac.il/%7Eronrubin/Publications/eusipco_avs.pdf

G. B. Rickard and . Taylor, The Long Wavelength Array, IEEE Proceedings, vol.97, pp.1421-1430, 2009.

M. Fadili and J. Starck, Monotone operator splitting for fast sparse solutions of inverse problems, SIAM Journal on Imaging Sciences, pp.2005-2006, 2009.

M. Fadili and J. Starck, EM algorithm for sparse representation-based image inpainting, IEEE International Conference on Image Processing 2005, pp.61-52, 2005.
DOI : 10.1109/ICIP.2005.1529991

URL : https://hal.archives-ouvertes.fr/hal-00013833

C. Fannjiang, Optimal arrays for compressed sensing in snapshot-mode radio interferometry, Astronomy & Astrophysics, vol.395, issue.59, pp.73-60, 2013.
DOI : 10.1111/j.1365-2966.2009.14665.x

R. Fender, A. Stewart, J. Macquart, I. Donnarumma, T. Murphy et al., Transient Astrophysics with the Square Kilometre Array. ArXiv e-prints, p.77, 2015.

R. P. Fender and M. E. Bell, Radio transients: an antediluvian review, Bulletin of the Astronomical Society of India, vol.39, pp.315-332, 2011.

R. Frieden, Restoring with Maximum Likelihood and Maximum Entropy*, Journal of the Optical Society of America, vol.62, issue.4
DOI : 10.1364/JOSA.62.000511

H. Garsden, J. Girard, S. Starck, C. Corbel, . Tasse et al., LOFAR sparse image reconstruction, Astronomy & Astrophysics, vol.550, issue.97, pp.90-2015
DOI : 10.1051/0004-6361/201220874

URL : https://hal.archives-ouvertes.fr/insu-01169967

J. Mckean and . Bobin, Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging, Journal of Instrumentation, vol.10, pp.8013-79, 2015.

S. Golbabaee, P. Arberet, and . Vandergheynst, Compressive Source Separation: Theory and Methods for Hyperspectral Imaging, IEEE Transactions on Image Processing, vol.22, issue.12, pp.5096-5110, 2013.
DOI : 10.1109/TIP.2013.2281405

URL : http://arxiv.org/pdf/1208.4505

M. Golbabaee and P. Vandergheynst, Compressed sensing of simultaneous low-rank and joint-sparse matrices. arXiv preprint, p.131, 2012.

L. Grobler, C. D. Nunhokee, O. M. Smirnov, A. J. Van-zyl, and A. G. De-bruyn, Calibration artefacts in radio interferometry ??? I. Ghost sources in Westerbork Synthesis Radio Telescope data, Monthly Notices of the Royal Astronomical Society, vol.509, issue.4, pp.4030-4047, 2014.
DOI : 10.1109/TSP.2009.2022894

A. Grossmann and J. Morlet, Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SIAM Journal on Mathematical Analysis, vol.15, issue.4, pp.723-736, 1984.
DOI : 10.1137/0515056

F. Gull and G. J. , Image reconstruction from incomplete and noisy data, Nature, vol.178, issue.5655, pp.686-690, 1978.
DOI : 10.1093/mnras/178.3.307

A. Haar, Zur Theorie der orthogonalen Funktionensysteme, Mathematische Annalen, vol.6, issue.3, pp.331-371, 1910.
DOI : 10.1007/BF01456326

URL : https://hal.archives-ouvertes.fr/hal-01333722

J. P. Hamaker, J. D. Bregman, and R. J. Sault, Understanding radio polarimetry. I. Mathematical foundations, Astronomy and Astrophysics Supplement Series, vol.117, issue.1, pp.137-147, 1978.
DOI : 10.1051/aas:1996146

URL : http://aas.aanda.org/articles/aas/pdf/2000/09/h1201.pdf

J. Stephen and . Hardy, Direct deconvolution of radio synthesis images using l1 minimisation, Astronomy & Astrophysics, vol.557, issue.59, pp.134-60, 2013.

J. A. Högbom, Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines, A&AS, vol.15, issue.58, pp.417-74, 1925.

M. Holschneider, R. Kronland-martinet, J. Morlet, and P. Tchamitchian, A real-time algorithm for signal analysis with the help of the wavelet transform, Wavelets, pp.286-297, 1989.

. Hyvarinen, Fast and robust fixed-point algorithms for independent component analysis, IEEE Transactions on Neural Networks, vol.10, issue.3, pp.626-634, 1999.
DOI : 10.1109/72.761722

URL : http://www.cs.helsinki.fi/u/ahyvarin/papers/TNN99_reprint.pdf

E. T. Jaynes, On the rationale of maximum-entropy methods, Proceedings of the IEEE, pp.939-952, 1982.
DOI : 10.1109/PROC.1982.12425

M. Jiang, J. N. Girard, J. L. Starck, S. Corbel, and C. Tasse, Compressed sensing and radio interferometry, 2015 23rd European Signal Processing Conference (EUSIPCO), pp.1646-1650, 2015.
DOI : 10.1109/EUSIPCO.2015.7362663

V. Kartik, A. Dabbech, J. Thiran, and Y. Wiaux, Robust dimensionality reduction for interferometric imaging of cygnus a, p.97, 2017.

M. Kleinsteuber and H. Shen, Blind Source Separation With Compressively Sensed Linear Mixtures, IEEE Signal Processing Letters, vol.19, issue.2, pp.107-110, 2012.
DOI : 10.1109/LSP.2011.2181945

URL : http://arxiv.org/pdf/1110.2593

K. Kokkinakis and A. K. Nandi, Multichannel blind deconvolution for source separation in convolutive mixtures of speech, IEEE Transactions on Audio, Speech and Language Processing, vol.14, issue.1, pp.200-212, 2006.
DOI : 10.1109/TSA.2005.854109

Z. Koldovsky and P. Tichavsky, Efficient variant of algorithm fastica for independent component analysis attaining the cramer-RAO lower bound, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, pp.1090-1095, 2005.
DOI : 10.1109/SSP.2005.1628758

S. Broderick, J. Corbel, S. Eislöffel, A. Markoff, J. D. Rowlinson et al., A LOFAR Census of Millisecond Pulsars. ArXiv e-prints, p.77, 2015.
URL : https://hal.archives-ouvertes.fr/insu-01321934

F. Lanusse, J. Starck, A. Leonard, and S. Pires, High resolution weak lensing mass mapping combining shear and flexion, Astronomy & Astrophysics, vol.38, pp.2-58, 2016.
DOI : 10.1007/s10444-011-9254-8

URL : http://www.aanda.org/articles/aa/pdf/2016/07/aa28278-16.pdf

J. Law, G. C. Bower, S. Burke-spolaor, B. Butler, E. Lawrence et al., A MILLISECOND INTERFEROMETRIC SEARCH FOR FAST RADIO BURSTS WITH THE VERY LARGE ARRAY, The Astrophysical Journal, vol.807, issue.1, p.95, 2015.
DOI : 10.1088/0004-637X/807/1/16

C. Lazarus, P. Weiss, N. Chauffert, F. Mauconduit, M. Bottlaender et al., Sparkling: Novel non-cartesian sampling schemes for accelerated 2d anatomical imaging at 7t using compressed sensing, 25th annua meeting of the International Society for Magnetic Resonance Imaging, p.146, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01577200

J. W. Lazio, T. E. Clarke, W. M. Lane, C. Gross, N. E. Kassim et al., Surveying the Dynamic Radio Sky with the Long Wavelength Demonstrator Array, AJ, vol.140140, issue.6, pp.1995-2006, 1995.

M. Samuel, J. Leach, C. Cardoso, . Baccigalupi, . Barreiro et al., Component separation methods for the planck mission, Astronomy & Astrophysics, vol.491, issue.2, pp.597-615, 2008.

M. Lederman and C. T. Hill, Quantum Physics for Poets

A. Leonard, F. Lanusse, and J. Starck, GLIMPSE: accurate 3D weak lensing reconstructions using sparsity, Monthly Notices of the Royal Astronomical Society, vol.428, issue.2, pp.1281-1294, 2014.
DOI : 10.1086/174279

URL : https://academic.oup.com/mnras/article-pdf/440/2/1281/18498127/stu273.pdf

A. Leonard, F. Lanusse, and J. Starck, Weak lensing reconstructions in 2D and 3D: implications for cluster studies, Monthly Notices of the Royal Astronomical Society, vol.428, issue.6816, pp.1146-1157, 2015.
DOI : 10.1086/174279

F. Li, T. J. Cornwell, and F. Hoog, The application of compressive sampling to radio astronomy i: Deconvolution. arXiv preprint, pp.59-75, 2011.

R. P. Linfield, IPM and ISM Coherence and Polarization Effects on Observations With Low-Frequency Space Arrays, The Astronomical Journal, vol.111, pp.2465-2475, 1996.
DOI : 10.1086/117981

URL : http://doi.org/10.1086/117981

D. R. Lorimer, A. Karastergiou, M. A. Mclaughlin, and S. Johnston, On the detectability of extragalactic fast radio transients, Monthly Notices of the Royal Astronomical Society: Letters, vol.157, issue.1, pp.5-9, 2013.
DOI : 10.1093/mnras/157.1.55

S. Makeig, A. J. Bell, T. Jung, and T. J. Sejnowski, Independent component analysis of electroencephalographic data, Advances in Neural Information Processing Systems, pp.145-151, 1996.

G. Stephane and . Mallat, Multiresolution approximations and wavelet orthonormal bases of ð??£ 2 (ð???) Transactions of the American mathematical society, pp.69-87, 1989.

B. Matei and Y. Meyer, A variant on the compressed sensing of emmanuel candes. Preprint Basarab Matei and Yves Meyer, A variant of the compressed sensing of Emmanuel Candès, p.58, 2008.

J. Mcewen and Y. Wiaux, Compressed sensing for wide-field radio interferometric imaging, Monthly Notices of the Royal Astronomical Society, vol.402, issue.2, pp.1318-1332, 2011.
DOI : 10.1111/j.1365-2966.2009.16079.x

J. Martin, T. J. Mckeown, and . Sejnowski, Independent component analysis of fmri data: examining the assumptions, Human brain mapping, vol.6, pp.5-6368, 1998.

A. Albert and . Michelson, Xxviii. visibility of interference-fringes in the focus of a telescope, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, pp.31256-259

J. Moreau, Proximit?? et dualit?? dans un espace hilbertien, Bulletin de la Société mathématique de France, vol.79, issue.2, pp.273-299, 1965.
DOI : 10.24033/bsmf.1625

D. Morris, M. Kramer, C. Thum, R. Wielebinski, M. Grewing et al., Pulsar detection at 87GHz, A&A, vol.322, pp.17-20, 1997.

F. Mottez and P. Zarka, Radio emissions from pulsar companions: a refutable explanation for galactic transients and fast radio bursts, Astronomy & Astrophysics, vol.780, issue.A86, p.76, 2014.
DOI : 10.1088/2041-8205/780/2/L21

URL : https://hal.archives-ouvertes.fr/hal-01053079

R. Narayan and R. Nityananda, Maximum entropy image restoration in astronomy. Annual review of astronomy and astrophysics, pp.127-170, 1986.

. Balas-kausik-natarajan, Sparse Approximate Solutions to Linear Systems, SIAM Journal on Computing, vol.24, issue.2, pp.227-234, 1995.
DOI : 10.1137/S0097539792240406

R. N. Neelamani, H. Choi, and R. Baraniuk, ForWaRD: Fourier-Wavelet Regularized Deconvolution for Ill-Conditioned Systems, IEEE Transactions on Signal Processing, vol.52, issue.2, pp.418-433, 2004.
DOI : 10.1109/TSP.2003.821103

URL : https://scholarship.rice.edu/bitstream/1911/20143/1/Nee2002Sep1ForWaRDFou.PDF

A. Onose, E. Rafael, A. Carrillo, . Repetti, D. Jason et al., Scalable splitting algorithms for big-data interferometric imaging in the SKA era, Monthly Notices of the Royal Astronomical Society, vol.463, issue.4, pp.4314-4335, 2016.
DOI : 10.1093/mnras/stv596

A. Onose, A. Dabbech, and Y. Wiaux, An accelerated splitting algorithm for radio-interferometric imaging: when natural and uniform weighting meet, Monthly Notices of the Royal Astronomical Society, vol.449, issue.1, pp.938-949, 2017.
DOI : 10.1093/mnras/stv596

URL : http://arxiv.org/pdf/1701.01748

N. Parikh and S. Boyd, Proximal Algorithms, Foundations and Trends?? in Optimization, vol.1, issue.3, pp.127-239, 2014.
DOI : 10.1561/2400000003

URL : http://www.nowpublishers.com/article/DownloadSummary/OPT-003

U. Pen and L. Connor, Local Circumnuclear Magnetar Solution to Extragalactic Fast Radio Bursts. ArXiv e-prints, p.76, 2015.
DOI : 10.1088/0004-637x/807/2/179

URL : http://iopscience.iop.org/article/10.1088/0004-637X/807/2/179/pdf

R. A. Perley, C. J. Chandler, B. J. Butler, and J. M. Wrobel, THE EXPANDED VERY LARGE ARRAY: A NEW TELESCOPE FOR NEW SCIENCE, The Astrophysical Journal, vol.739, issue.1
DOI : 10.1088/2041-8205/739/1/L1

E. Petroff, M. Bailes, E. D. Barr, B. R. Barsdell, N. D. Bhat et al., A real-time fast radio burst: polarization detection and multiwavelength follow-up, Monthly Notices of the Royal Astronomical Society, vol.118, issue.1, pp.246-255, 2015.
DOI : 10.1086/510102

URL : https://academic.oup.com/mnras/article-pdf/447/1/246/4918382/stu2419.pdf

S. Pires, S. Mathur, A. Rafael, J. García, D. Ballot et al., Gap interpolation by inpainting methods: Application to ground and space-based asteroseismic data, Astronomy & Astrophysics, vol.496, p.18, 2015.
DOI : 10.1051/0004-6361:200811296

URL : https://hal.archives-ouvertes.fr/cea-01290087

S. J. Prasad and . Wijnholds, Amsterdam-ASTRON radio transient facility and analysis centre: towards a 24 x 7, all-sky monitor for the low-frequency array (LOFAR), Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.39, issue.1992, 2013.
DOI : 10.1109/78.97999

U. Rau and T. J. Cornwell, A multi-scale multi-frequency deconvolution algorithm for synthesis imaging in radio interferometry, Astronomy & Astrophysics, vol.527, pp.71-75, 2011.
DOI : 10.1051/0004-6361/201016082

U. Rau and T. J. Cornwell, A multi-scale multi-frequency deconvolution algorithm for synthesis imaging in radio interferometry, Astronomy & Astrophysics, vol.527, pp.71-132, 2011.
DOI : 10.1051/0004-6361/201016082

A. Repetti, J. Birdi, A. Dabbech, and Y. Wiaux, A non-convex optimization algorithm for joint dde calibration and imaging in radio interferometry, p.75, 2017.

A. Robinson, The Last Man who Knew Everything: Thomas Young, the Anonymous Polymath who Proved Newton Wrong, Explained how We See, Cured the Sick, and Deciphered the Rosetta Stone, Among Other Feats of Genius, 2006.

M. Ryle and D. Vonberg, Solar radiation on 175 mc./s, Classics in Radio Astronomy, pp.184-187, 1946.

M. Ryle, J. Hewish, and . Shakeshaft, The synthesis of large radio telescopes by the use of radio interferometers, IRE Transactions on Antennas and Propagation, vol.7, issue.5, pp.120-124, 1959.
DOI : 10.1109/TAP.1959.1144745

M. Ryle and A. Hewish, The Synthesis of Large Radio Telescopes, Monthly Notices of the Royal Astronomical Society, vol.120, issue.3, pp.220-230, 1960.
DOI : 10.1093/mnras/120.3.220

L. H. Scheers, Transient and variable radio sources in the LOFAR sky: An architecture for a detection framework, p.77, 2011.

F. R. Schwab, Optimal Gridding of Visibility Data in Radio Interferometry, Indirect Imaging. Measurement and Processing for Indirect Imaging, pp.333-346, 1984.

F. R. Schwab, Relaxing the isoplanatism assumption in self-calibration; applications to low-frequency radio interferometry, The Astronomical Journal, vol.89, pp.1076-1081, 1984.
DOI : 10.1086/113605

W. Ivan, . Selesnick, A. Mario, and . Figueiredo, Signal restoration with overcomplete wavelet transforms: Comparison of analysis and synthesis priors, Proceedings of SPIE, p.49, 2009.

J. Mark and . Shensa, The discrete wavelet transform: wedding the a trous and mallat algorithms, IEEE Transactions on signal processing, vol.40, issue.10, pp.2464-2482, 1992.

E. Slezak, A. De-lapparent, and . Bijaoui, Objective detection of voids and high-density structures in the first CfA redshift survey slice, The Astrophysical Journal, vol.409, pp.517-529, 1993.
DOI : 10.1086/172683

M. Smirnov, Revisiting the radio interferometer measurement equation, Astronomy & Astrophysics, vol.527, pp.106-78, 2011.
DOI : 10.1051/0004-6361/201016082

URL : http://www.aanda.org/articles/aa/pdf/2011/03/aa16082-10.pdf

J. N. Spreeuw, Search and detection of low frequency radio transientsk, p.77, 2010.

J. Starck and F. Murtagh, Image restoration with noise suppression using the wavelet transform, Astronomy and Astrophysics -A&A, vol.288, pp.342-348, 1994.

J. Starck and F. Murtagh, Astronomical image and data analysis, p.44, 2007.
DOI : 10.1007/978-3-540-33025-7

J. L. Starck, D. L. Donoho, and E. J. Candès, Astronomical image representation by the curvelet transform, Astronomy & Astrophysics, vol.11, issue.6, pp.785-800, 2003.
DOI : 10.1017/CBO9780511564352

URL : http://www.aanda.org/articles/aa/pdf/2003/05/aa2574.pdf

J. Starck, M. Elad, L. David, and . Donoho, Image decomposition via the combination of sparse representations and a variational approach, IEEE Transactions on Image Processing, vol.14, issue.10, pp.1570-1582, 2005.
DOI : 10.1109/TIP.2005.852206

J. Starck, J. M. Fadili, S. Digel, B. Zhang, and J. Chiang, Source detection using a 3D sparse representation: application to the Fermi gamma-ray space telescope, Astronomy & Astrophysics, vol.5, issue.2, pp.641-652, 2009.
DOI : 10.1016/j.stamet.2008.02.004

URL : https://hal.archives-ouvertes.fr/hal-00813995

J. Starck, M. J. Murtagh, and M. Bertero, The Starlet Transform in Astronomical Data Processing: Application to Source Detection and Image Deconvolution, pp.1489-1531, 2011.

J. Starck, J. Emmanuel, . Candès, L. David, and . Donoho, The curvelet transform for image denoising, IEEE Transactions on Image Processing, vol.11, issue.6, pp.670-684, 2002.
DOI : 10.1109/TIP.2002.1014998

J. Starck, M. Elad, and D. Donoho, Redundant multiscale transforms and their application for morphological component separation Advances in Imaging and Electron Physics, pp.287-348, 2004.

J. Starck, J. Fadili, and F. Murtagh, The Undecimated Wavelet Decomposition and its Reconstruction, IEEE Transactions on Image Processing, vol.16, issue.2, pp.297-309, 2007.
DOI : 10.1109/TIP.2006.887733

URL : https://hal.archives-ouvertes.fr/hal-00080092

J. Starck, F. Murtagh, and J. Fadili, Sparse image and signal processing: Wavelets and related geometric multiscale analysis, p.55, 2015.
DOI : 10.1017/CBO9781316104514

URL : https://hal.archives-ouvertes.fr/hal-01658853

R. A. Stewart, R. Wijers, P. Wijnands, and . Zarka, The LOFAR Transients Pipeline, Astronomy and Computing, vol.11, pp.25-48, 2015.
URL : https://hal.archives-ouvertes.fr/insu-01178502

N. Mujahid, . Syed, G. Pando, . Georgiev, M. Panos et al., Blind signal separation methods in computational neuroscience. Modern Electroencephalographic Assessment Techniques: Theory and Applications, pp.291-322, 2015.

G. Tasse, S. Van-diepen, R. J. Van-der-tol, J. E. Van-weeren, F. Van-zwieten et al., LOFAR calibration and wide-field imaging, Comptes Rendus Physique, vol.13, issue.1, pp.28-32, 2012.
DOI : 10.1016/j.crhy.2011.10.006

URL : https://hal.archives-ouvertes.fr/hal-00721922

S. Tasse, J. Van-der-tol, G. Van-zwieten, S. Van-diepen, and . Bhatnagar, Applying full polarization A-Projection to very wide field of view instruments: An imager for LOFAR, Astronomy & Astrophysics, vol.759, issue.78, pp.105-79, 2013.
DOI : 10.1088/0004-637X/759/1/17

B. Greg, C. L. Taylor, . Carilli, A. Richard, and . Perley, Synthesis imaging in radio astronomy ii, Synthesis Imaging in Radio Astronomy II, p.26, 1999.

. Mitchell, The Murchison Widefield Array, Proceedings of RFI mitigation workshop ??? PoS(RFI2010), p.7, 2013.
DOI : 10.22323/1.107.0016

A. Tonazzini, I. Gerace, and F. Martinelli, Multichannel Blind Separation and Deconvolution of Images for Document Analysis, IEEE Transactions on Image Processing, vol.19, issue.4, pp.912-925, 2010.
DOI : 10.1109/TIP.2009.2038814

. Tseng, Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization, Journal of Optimization Theory and Applications, vol.109, issue.3, pp.475-494, 2001.
DOI : 10.1023/A:1017501703105

M. Vetterli, Filter banks allowing perfect reconstruction, Signal Processing, vol.10, issue.3, pp.219-244, 1986.
DOI : 10.1016/0165-1684(86)90101-5

S. Vijay-kartik, E. Rafael, J. Carrillo, Y. Thiran, and . Wiaux, A Fourier dimensionality reduction model for big data interferometric imaging, Monthly Notices of the Royal Astronomical Society, vol.33, issue.2, pp.2382-2400, 2017.
DOI : 10.1137/090777761

E. Vincent, R. Gribonval, and C. Févotte, Performance measurement in blind audio source separation, IEEE Transactions on Audio, Speech and Language Processing, vol.14, issue.4, pp.1462-1469, 2006.
DOI : 10.1109/TSA.2005.858005

URL : https://hal.archives-ouvertes.fr/inria-00544230

C. Bang and . V?uv?u, A splitting algorithm for dual monotone inclusions involving cocoercive operators, Advances in Computational Mathematics, vol.69, issue.106, pp.1-15, 2013.

Z. Wang, A. C. Bovik, R. Hamid, . Sheikh, P. Eero et al., Image Quality Assessment: From Error Visibility to Structural Similarity, IEEE Transactions on Image Processing, vol.13, issue.4, pp.600-612, 2004.
DOI : 10.1109/TIP.2003.819861

URL : http://www.cns.nyu.edu/~zwang/files/papers/ssim.pdf

U. Wenger, M. Rau, and . Magnor, A group sparsity imaging algorithm for transient radio sources, Astronomy and Computing, vol.1, pp.40-45, 2013.
DOI : 10.1016/j.ascom.2013.02.002

URL : http://workshops.fhr.fraunhofer.de/cosera/pdf/A2_2.pdf

S. Wenger, M. Magnor, Y. Pihlström, U. Bhatnagar, and . Rau, Sparseri: A compressed sensing framework for aperture synthesis imaging in radio astronomy . Publications of the Astronomical Society of the Pacific, pp.1367-60, 2010.

J. Wernecke and L. R. , Maximum Entropy Image Reconstruction, IEEE Transactions on Computers, vol.26, issue.4, pp.351-364, 1977.
DOI : 10.1109/TC.1977.1674845

Y. Wiaux, L. Jacques, G. Puy, M. Anna, P. Scaife et al., Compressed sensing imaging techniques for radio interferometry, Monthly Notices of the Royal Astronomical Society, vol.31, issue.3
DOI : 10.1093/mnras/120.3.220

URL : https://hal.archives-ouvertes.fr/inria-00369428

Y. Wiaux, G. Puy, Y. Boursier, and P. Vandergheynst, Spread spectrum for imaging techniques in radio interferometry, Monthly Notices of the Royal Astronomical Society, vol.395, issue.2, pp.1029-1038, 2009.
DOI : 10.1093/mnras/120.3.220

URL : https://academic.oup.com/mnras/article-pdf/400/2/1029/3344627/mnras0400-1029.pdf

G. Woan, Capabilities and limitations of long wavelength observations from space
DOI : 10.1093/mnras/166.3.499

P. Zarka, J. N. Girard, M. Tagger, L. Denis, . Lss et al., The LOFAR Super Station project in Nançay, SF2A-2012: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics, pp.687-694, 2012.

M. Zibulevsky and B. Pearlmutter, Blind Source Separation by Sparse Decomposition in a Signal Dictionary, Neural Computation, vol.1, issue.4, pp.863-882, 2001.
DOI : 10.1016/S0042-6989(97)00169-7