F. Fazekas, R. Kleinert, G. Roob, G. Kleinert, P. Kapeller et al., Histopathologic analysis of foci of signal loss on gradient-echo t2*-weighted mr images in patients with spontaneous intracerebral hemorrhage: evidence of microangiopathy-related microbleeds, American Journal of Neuroradiology, vol.20, issue.4, pp.637-642, 1999.

F. Bloch, Nuclear induction, Phys. Rev, vol.70, pp.460-474, 1946.

D. A. Feinberg, J. Hale, J. Watts, L. Kaufman, and A. Mark, Halving mr imaging time by conjugation: demonstration at 3.5 kg, Radiology, vol.161, issue.2, pp.527-531, 1986.

K. Pruessmann, P. Weiger, M. Scheidegger, and P. Boesiger, SENSE: sensitivity encoding for fast MRI, Magnetic Resonance in Medicine, vol.42, issue.5, pp.952-962, 1999.

M. A. Griswold, P. M. Jakob, R. M. Heidemann, M. Nittka, V. Jellus et al., Generalized autocalibrating partially parallel acquisitions (grappa), Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, vol.47, issue.6, pp.1202-1210, 2002.

F. A. Breuer, M. Blaimer, M. F. Mueller, N. Seiberlich, R. M. Heidemann et al., Controlled aliasing in volumetric parallel imaging, vol.55, pp.549-556, 2006.

D. Donoho, Compressed sensing, IEEE Transactions on Information Theory, vol.52, issue.4, pp.1289-1306, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00369486

M. Lustig, D. Donoho, and J. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging, Magnetic Resonance in Medicine, vol.58, issue.6, pp.1182-1195, 2007.

J. H. Lee, B. A. Hargreaves, B. S. Hu, and D. G. Nishimura, Fast 3D imaging using variable-density spiral trajectories with applications to limb perfusion, Magnetic Resonance in Medicine, vol.50, issue.6, pp.1276-1285, 2003.

C. Lazarus, P. Weiss, N. Chauffert, F. Mauconduit, L. E. Gueddari et al., Sparkling: variable-density k-space filling curves for accelerated t2*-weighted mri, 2019.

J. Fessler and B. Sutton, Nonuniform fast Fourier transforms using min-max interpolation, 2003.

J. Keiner, S. Kunis, and D. Potts, Using NFFT 3-a software library for various nonequispaced fast fourier transforms, ACM Transactions on Mathematical Software (TOMS), vol.36, issue.4, p.19, 2009.

M. Guerquin-kern, M. Haberlin, K. P. Pruessmann, and M. Unser, A fast wavelet-based reconstruction method for magnetic resonance imaging, IEEE transactions on medical imaging, vol.30, issue.9, pp.1649-1660, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01813870

L. Chaâri, J. Pesquet, A. Benazza-benyahia, and P. Ciuciu, A wavelet-based regularized reconstruction algorithm for sense parallel mri with applications to neuroimaging, Medical image analysis, vol.15, issue.2, pp.185-201, 2011.

M. Hansen and T. Srensen, Gadgetron: An open source framework for medical image reconstruction, Magnetic Resonance in Medicine, vol.69, issue.6, pp.1768-1776

L. E. Gueddari, P. Ciuciu, E. Chouzenoux, A. Vignaud, and J. Pesquet, Calibrationless oscar-based image reconstruction in compressed sensing parallel mri, IEEE International Symposium of Biomedical Imaging, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02101262

J. Moreau, Bulletin de la Société mathématique de France 93, pp.273-299, 1965.

M. A. Bernstein, K. F. King, and X. J. Zhou, Handbook of MRI pulse sequences, 2004.

G. Puy, P. Vandergheynst, and Y. Wiaux, On variable density compressive sampling, IEEE Signal Processing Letters, vol.18, issue.10, pp.595-598, 2011.

N. Chauffert, P. Ciuciu, J. Kahn, and P. Weiss, Variable density sampling with continuous trajectories. Application to MRI, SIAM Journal on Imaging Sciences, vol.7, pp.1962-1992, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00908486

C. Boyer, N. Chauffert, P. Ciuciu, J. Kahn, and P. Weiss, On the generation of sampling schemes for Magnetic Resonance Imaging, SIAM Journal on Imaging Sciences, vol.9, issue.4, pp.2039-2072, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01373758

N. Pustelnik, A. Benazza-benhayia, Y. Zheng, and J. Pesquet, Wavelet-based image deconvolution and reconstruction, Wiley Encyclopedia of Electrical and Electronics Engineering, pp.1-34, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01164833

A. Florescu, E. Chouzenoux, J. Pesquet, P. Ciuciu, and S. Ciochina, A majorize-minimize memory gradient method for complex-valued inverse problems, Signal Processing, vol.103, pp.285-295, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00829788

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

I. Daubechies, M. Defrise, and C. De-mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, vol.57, issue.11, pp.1413-1457, 2004.

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.

A. B. Taylor, J. M. Hendrickx, and F. Glineur, Exact worst-case performance of first-order methods for composite convex optimization, SIAM Journal on Optimization, vol.27, issue.3, pp.1283-1313, 2017.

P. L. Combettes and J. Pesquet, Stochastic approximations and perturbations in forward-backward splitting for monotone operators, Pure and Applied Functional Analysis, vol.1, issue.1, pp.13-37, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01380000

J. Eckstein and D. P. Bertsekas, On the douglasrachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, vol.55, issue.1-3, pp.293-318, 1992.

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.40, issue.1, pp.120-145, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00490826

L. Condat, A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms, Journal of Optimization Theory and Applications, vol.158, issue.2, pp.460-479, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00609728

B. V?, A splitting algorithm for dual monotone inclusions involving cocoercive operators, Advances in Computational Mathematics, vol.38, pp.667-681, 2013.

M. Elad, P. Milanfar, and R. Rubinstein, Analysis versus synthesis in signal priors, Inverse problems, vol.23, issue.3, p.947, 2007.

L. Condat, A primal-dual splitting method for convex optimization involving lipschitzian, proximable and linear composite terms, Journal of Optimization Theory and Applications, vol.158, pp.460-479, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00609728

W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing, 2007.

H. Cherkaoui, L. E. Gueddari, C. Lazarus, A. Grigis, F. Poupon et al., Analysis vs synthesis-based regularization for combined compressed sensing and parallel MRI reconstruction at 7 tesla, 26th European Signal Processing Conference, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01800700

P. Roemer, W. Edelstein, C. Hayes, S. Souza, and O. Mueller, The NMR phased array, Magnetic resonance in medicine, vol.16, issue.2, pp.192-225, 1990.

M. Uecker, P. Lai, M. Murphy, P. Virtue, M. Elad et al., ESPIRiT-an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA, Magnetic Resonance in Medicine, vol.71, issue.3, pp.990-1001, 2014.

L. E. Gueddari, C. Lazarus, H. Carrié, A. Vignaud, and P. Ciuciu, Self-calibrating nonlinear reconstruction algorithms for variable density sampling and parallel reception MRI, 10th IEEE SAM workshop, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01782428

H. She, R. Chen, D. Liang, E. Dibella, and L. Ying, Sparse BLIP: Blind iterative parallel imaging reconstruction using compressed sensing, Magnetic Resonance in Medicine, vol.71, issue.2, pp.645-660, 2014.

J. Haldar, Low-rank modeling of local k-space neighborhoods (LORAKS) for Constrained MRI, IEEE transactions on Medical Imaging, vol.33, issue.3, pp.668-681, 2014.

P. J. Shin, P. E. Larson, M. A. Ohliger, M. Elad, J. M. Pauly et al., Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion, Magnetic resonance in medicine, vol.72, issue.4, pp.959-970, 2014.

D. Lee, K. H. Jin, E. Y. Kim, S. Park, and J. C. Ye, Acceleration of mr parameter mapping using annihilating filter-based low rank hankel matrix (aloha), Magnetic resonance in medicine, vol.76, issue.6, pp.1848-1864, 2016.

A. Majumdar and R. Ward, Calibration-less multi-coil MR image reconstruction, Magnetic Resonance in Medicine, vol.30, issue.7, pp.1032-1045, 2012.

J. Trzasko and A. Manduca, Calibrationless parallel MRI using CLEAR, Signals, Systems and Computers (ASILOMAR), 2011 Conference Record of the Forty Fifth Asilomar Conference on, pp.75-79, 2011.

N. Seiberlich, F. A. Breuer, M. Blaimer, K. Barkauskas, P. Jakob et al., Non-cartesian data reconstruction using GRAPPA operator gridding (GROG), Magnetic Resonance in Medicine, vol.58, issue.6, pp.1257-1265, 2007.

X. Zeng and M. Figueiredo, The ordered weighted l1 norm: Atomic formulation, projections, and algorithms, 2014.

S. Winkelmann, T. Schaeffter, T. Koehler, H. Eggers, and O. Doessel, An optimal radial profile order based on the golden ratio for time-resolved mri, IEEE transactions on medical imaging, vol.26, issue.1, pp.68-76, 2006.

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, Image quality assessment: from error visibility to structural similarity, IEEE transactions on Image Processing, vol.13, issue.4, pp.600-612, 2004.

C. M. Stein, Estimation of the mean of a multivariate normal distribution, The annals of Statistics, pp.1135-1151, 1981.

T. Hastie, R. Tibshirani, J. Friedman, and J. Franklin, The elements of statistical learning: data mining, inference and prediction, The Mathematical Intelligencer, vol.27, issue.2, pp.83-85, 2005.

J. Lin, Python non-uniform fast Fourier transform (PyNUFFT): An accelerated non-Cartesian MRI package on a heterogeneous platform (CPU/GPU), Journal of Imaging, vol.4, issue.3, p.51, 2018.

J. Sun, H. Li, and Z. Xu, Deep admm-net for compressive sensing MRI, Advances in neural information processing systems, pp.10-18, 2016.

M. Mardani, E. Gong, J. Y. Cheng, S. S. Vasanawala, G. Zaharchuk et al., Deep generative adversarial neural networks for compressive sensing MRI, IEEE transactions on medical imaging, vol.38, issue.1, pp.167-179, 2018.

K. Hammernik, T. Klatzer, E. Kobler, M. P. Recht, D. K. Sodickson et al., Learning a variational network for reconstruction of accelerated MRI data, Magnetic resonance in medicine, vol.79, issue.6, pp.3055-3071, 2018.

B. Zhu, J. Z. Liu, S. F. Cauley, B. R. Rosen, and M. S. Rosen, Image reconstruction by domain-transform manifold learning, Nature, vol.555, issue.7697, p.487, 2018.

J. A. Fessler and D. C. Noll, Iterative reconstruction methods for non-cartesian mri, Proc. ISMRM Workshop on Non-Cartesian MRI, 2007.

M. Buehrer, K. P. Pruessmann, P. Boesiger, and S. Kozerke, Array compression for mri with large coil arrays, Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, vol.57, issue.6, pp.1131-1139, 2007.