H. Attouch, J. Bolte, P. Redont, and A. Soubeyran, Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-??ojasiewicz Inequality, Mathematics of Operations Research, vol.35, issue.2, pp.438-457, 2010.
DOI : 10.1287/moor.1100.0449

A. Beck and M. Teboulle, Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems, IEEE Transactions on Image Processing, vol.18, issue.11, pp.2419-2434, 2009.
DOI : 10.1109/TIP.2009.2028250

J. Bect, L. Blanc-feraud, G. Aubert, and A. Chambolle, A l1-unified variational framework for image restoration, Proceedings of the 8th European Conference on Computer Vision, pp.1-13, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00217251

R. Benedetti and J. Risler, Real algebraic and semi-algebraic sets. Actualités mathématiques. Hermann, 1990.

L. Berdondini, K. Imfeld, A. Maccione, M. Tedesco, S. Neukom et al., Active pixel sensor array for high spatio-temporal resolution electrophysiological recordings from single cell to large scale neuronal networks, Lab on a Chip, vol.3, issue.18, pp.92644-2651, 2009.
DOI : 10.1002/acs.1077

M. Bergounioux and L. Piffet, A Second-Order Model for Image Denoising. Set-Valued and Variational Analysis, pp.277-306, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00440872

J. Bolte, A. Daniilidis, and A. Lewis, The ??ojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems, SIAM Journal on Optimization, vol.17, issue.4, pp.1205-1223, 2007.
DOI : 10.1137/050644641

J. Bolte, A. Daniilidis, A. Lewis, and M. Shiota, Clarke Subgradients of Stratifiable Functions, SIAM Journal on Optimization, vol.18, issue.2, pp.556-572, 2007.
DOI : 10.1137/060670080

S. Boyd, Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Machine Learning, pp.1-122, 2010.
DOI : 10.1561/2200000016

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext, 2010.

D. A. Butts, C. Weng, J. Jin, J. Alonso, and L. Paninski, Temporal Precision in the Visual Pathway through the Interplay of Excitation and Stimulus-Driven Suppression, Journal of Neuroscience, vol.31, issue.31, pp.3111313-11327, 2011.
DOI : 10.1523/JNEUROSCI.0434-11.2011

E. J. Candes, M. B. Wakin, and S. P. Boyd, Enhancing Sparsity by Reweighted ??? 1 Minimization, Journal of Fourier Analysis and Applications, vol.7, issue.3, pp.5-6877, 2008.
DOI : 10.1007/s00041-008-9045-x

M. Carandini, J. B. Demb, V. Mante, D. J. Tollhurst, Y. Dan et al., Do We Know What the Early Visual System Does?, Journal of Neuroscience, vol.25, issue.46, pp.2510577-10597, 2005.
DOI : 10.1523/JNEUROSCI.3726-05.2005

A. Chambolle, An Algorithm for Total Variation Minimization and Applications, J. Math. Imaging Vis, vol.20, issue.12, pp.89-97, 2004.

E. Chichilnisky, A simple white noise analysis of neuronal light responses, Network: Computation in Neural Systems, vol.12, issue.2, pp.199-213, 2001.
DOI : 10.1080/713663221

P. L. Combettes and J. Pesquet, Proximal Splitting Methods in Signal Processing, Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212, 2011.
DOI : 10.1007/978-1-4419-9569-8_10

URL : https://hal.archives-ouvertes.fr/hal-00643807

L. Dries, Tame topology and o-minimal structures. Number 248 in London Mathematical Society lecture note series, p.550530719, 2003.

I. Ekeland and R. Temam, Analyse convexe et problèmes variationnels, Etudes mathématiques . Dunod, 1974.

C. Enroth-cugell and J. G. Robson, The contrast sensitivity of retinal ganglion cells of the cat, The Journal of Physiology, vol.187, issue.3, pp.517-552, 1966.
DOI : 10.1113/jphysiol.1966.sp008107

W. Gerstner and W. Kistler, Spiking Neuron Models, 2002.

T. Gollisch and M. Meister, Eye Smarter than Scientists Believed: Neural Computations in Circuits of the Retina, Neuron, vol.65, issue.2, pp.150-164, 2010.
DOI : 10.1016/j.neuron.2009.12.009

G. Hilgen, S. Pirmoradian, D. Pamplona, P. Kornprobst, B. Cessac et al., Pan-retinal characterization of light responses from ganglion cells in the developing mouse retina. bioRxiv, 2016.

A. Maccione, M. H. Hennig, M. Gandolfo, O. Muthmann, J. Coppenhagen et al., Following the ontogeny of retinal waves: pan-retinal recordings of population dynamics in the neonatal mouse, The Journal of Physiology, vol.20, issue.7, pp.5921545-1563, 2014.
DOI : 10.1113/jphysiol.2013.262840

R. H. Masland, Cell Populations of the Retina: The Proctor Lecture, Investigative Opthalmology & Visual Science, vol.52, issue.7, pp.4581-4591, 2011.
DOI : 10.1167/iovs.10-7083

J. Mcfarland, Y. Cui, and D. A. Butts, Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs, PLoS Computational Biology, vol.78, issue.7, p.1003143, 2013.
DOI : 10.1371/journal.pcbi.1003143.s006

J. Mcfarland, Y. Cui, and D. Butts, Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs, PLoS Computational Biology, vol.78, issue.7, p.2013
DOI : 10.1371/journal.pcbi.1003143.s006

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

Y. Nesterov, Gradient methods for minimizing composite functions, Mathematical Programming, pp.125-161, 2013.
DOI : 10.1007/s10107-012-0629-5

D. Pamplona, G. Hilgen, S. Pirmoradian, M. Hennig, B. Cessac et al., A super-resolution approach for receptive fields estimation of neuronal ensembles, BMC Neuroscience, vol.16, issue.Suppl 1, 2015.
DOI : 10.1186/1471-2202-16-S1-P130

URL : https://hal.archives-ouvertes.fr/hal-01215541

L. Paninski, Maximum likelihood estimation of cascade point-process neural encoding models, Network: Computation in Neural Systems, vol.15, issue.4, pp.243-262, 2004.
DOI : 10.1088/0954-898X_15_4_002

L. Paninski, J. Pillow, and J. Lewi, Statistical models for neural encoding, decoding, and optimal stimulus design, Prog Brain Res, vol.165, pp.493-507, 2007.
DOI : 10.1016/S0079-6123(06)65031-0

M. Park and J. W. Pillow, Receptive Field Inference with Localized Priors, PLoS Computational Biology, vol.23, issue.10, p.1002219, 2011.
DOI : 10.1371/journal.pcbi.1002219.s002

URL : http://doi.org/10.1371/journal.pcbi.1002219

Z. Peng, Y. Xu, M. Yan, and W. Yin, ARock: An Algorithmic Framework for Asynchronous Parallel Coordinate Updates, 35] J. Pillow. Likelihood-based approaches to modeling the neural code. Bayesian brain: Probabilistic approaches to neural coding, pp.53-70, 2007.
DOI : 10.1137/15M1024950

URL : http://arxiv.org/abs/1506.02396

J. Pillow, L. Paninski, V. Uzzell, E. Simoncelli, and E. Chichilnisky, Prediction and Decoding of Retinal Ganglion Cell Responses with a Probabilistic Spiking Model, Journal of Neuroscience, vol.25, issue.47, pp.11003-11013, 2005.
DOI : 10.1523/JNEUROSCI.3305-05.2005

J. Pillow, J. Shlens, L. Paninski, A. Sher, A. Litke et al., Spatio-temporal correlations and visual signalling in a complete neuronal population, Nature, vol.22, issue.7207, pp.454995-999, 2008.
DOI : 10.1038/nature07140

R. Rockafellar and R. Wets, Variational Analysis, volume 317 of Grundlehren der mathematischen Wissenschaften, 1998.

R. Rodieck, Quantitative analysis of cat retinal ganglion cell response to visual stimuli, Vision Research, vol.5, issue.12, pp.583-601, 1965.
DOI : 10.1016/0042-6989(65)90033-7

E. Simoncelli, L. Paninski, J. Pillow, and O. Schwartz, The Cognitive Neurosciences, 3rd edition, chapter Characterization of neural responses with stochastic stimuli, 2004.

W. Su, S. Boyd, and E. Candes, A differential equation for modeling nesterov's accelerated gradient method: Theory and insights

A. Wilkie, MODEL COMPLETENESS RESULTS FOR EXPANSIONS OF THE ORDERED FIELD OF REAL NUMBERS BY RESTRICTED PFAFFIAN FUNCTIONS AND THE EXPONENTIAL FUNCTION, Journal of the American Mathematical Society, vol.9, issue.4, pp.1051-1094, 1996.
DOI : 10.1142/9789812564894_0029

A. Wohrer, Model and large-scale simulator of a biological retina with contrast gain control, 2008.

A. Wohrer and P. Kornprobst, Virtual Retina: A biological retina model and simulator, with contrast gain control, Journal of Computational Neuroscience, vol.32, issue.3, pp.219-249, 2009.
DOI : 10.1007/s10827-008-0108-4

URL : https://hal.archives-ouvertes.fr/inria-00160716