A. Alvera-azcarate, A. Barth, M. Rixen, and J. M. Beckers, Reconstruction of incomplete oceanographic data sets using empirical orthogonal functions: application to the Adriatic Sea surface temperature, Ocean Modelling, vol.9, issue.4, pp.325-346, 2005.
DOI : 10.1016/j.ocemod.2004.08.001

E. Autret and J. Piolle, Product User Manual for ODYSSEA Level 3 and 4 global and regional products

T. Ifremer and /. Cersat, Available online at: http://projets.ifremer.fr/cersat/Data/Discovery/By-parameter/Sea-surface- temperature/ODYSSEA-Global-SST-Analysis, 2011.

D. Sirjacobs, A. Alvera-azcarate, A. Barth, G. Lacroix, Y. Park et al., Cloud filling of ocean colour and sea surface temperature remote sensing products over the Southern North Sea by the Data Interpolating Empirical Orthogonal Functions methodology, Journal of Sea Research, vol.65, issue.1
DOI : 10.1016/j.seares.2010.08.002

S. Ba, . Autret, B. Chapron, and R. Fablet, Statistical Descriptors of Ocean Regimes From the Geometric Regularity of SST Observations, IEEE Geoscience and Remote Sensing Letters, vol.9, issue.5, pp.851-854, 2012.
DOI : 10.1109/LGRS.2012.2184258

URL : https://hal.archives-ouvertes.fr/hal-00945379

A. Buades, B. Coll, and J. M. Morel, A Non-Local Algorithm for Image Denoising, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), 2005.
DOI : 10.1109/CVPR.2005.38

D. Bernard, G. Boffetta, A. Celani, and G. Falkovich, Conformal invariance in two-dimensional turbulence, Nature Physics, vol.94, issue.2, pp.124-128, 2006.
DOI : 10.1038/nphys217

URL : https://hal.archives-ouvertes.fr/hal-00018847

J. Byung-tae-oh and C. Kuo, Super-resolution texture synthesis using stochastic PAR/NL model, J Vis. Comp. Repr, vol.23, issue.7, pp.995-1007, 2012.

V. Caselles, J. M. Morel, and C. Sbert, An axiomatic approach to image interpolation, IEEE Transactions on Image Processing, vol.7, issue.3, pp.376-386, 1998.
DOI : 10.1109/83.661188

P. Chainais, E. Konig, V. Delouille, and J. Hochedez, Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes, Journal of Mathematical Imaging and Vision, vol.89, issue.8, pp.28-44, 2011.
DOI : 10.1007/s10851-010-0222-6

URL : https://hal.archives-ouvertes.fr/hal-00707631

A. Criminisi, P. Perez, and K. Toyama, Region Filling and Object Removal by Exemplar-Based Image Inpainting, IEEE Transactions on Image Processing, vol.13, issue.9, pp.1200-1212, 2004.
DOI : 10.1109/TIP.2004.833105

C. Deledalle, L. Denis, F. Tupin, and . Nl-insar, NL-InSAR: Nonlocal Interferogram Estimation, IEEE Transactions on Geoscience and Remote Sensing, vol.49, issue.4, pp.1441-1452
DOI : 10.1109/TGRS.2010.2076376

URL : https://hal.archives-ouvertes.fr/hal-00957980

A. A. Efros and W. Freeman, Image quilting for texture synthesis and transfer, Proceedings of the 28th annual conference on Computer graphics and interactive techniques , SIGGRAPH '01, 2001.
DOI : 10.1145/383259.383296

R. Fablet, B. Boussidi, E. Autret, and B. Chapron, Random walk models for geometry-driven image super-resolution, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, 2013.
DOI : 10.1109/ICASSP.2013.6638046

URL : https://hal.archives-ouvertes.fr/hal-00960533

W. T. Freeman and C. Liu, Markov Random Fields for Super-resolution and Texture Synthesis, Advances in Markov Random Fields for Vision and Image Processing, 2011.

B. Galerne, Y. Gousseau, and J. M. Morel, Random Phase Textures: Theory and Synthesis, IEEE Transactions on Image Processing, vol.20, issue.1, 2011.
DOI : 10.1109/TIP.2010.2052822

URL : https://hal.archives-ouvertes.fr/hal-00418389

D. Glasner, S. Bagon, and M. Irani, Super-resolution from a single image, 2009 IEEE 12th International Conference on Computer Vision, 2009.
DOI : 10.1109/ICCV.2009.5459271

H. He and W. Siu, Single image super-resolution using Gaussian process regression, CVPR 2011, pp.449-456
DOI : 10.1109/CVPR.2011.5995713

D. J. Heeger and J. Bergen, Pyramid Based Texture Analysis/Synthesis, Proc. ACM SIGGRAPH, pp.229-238, 1995.
DOI : 10.1109/icip.1995.537718

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.1445

A. N. Kolmogorov, The local structure of turbulence in in-compressible viscous fluid for very large reynolds numbers, 1941.

G. Lapeyre and P. Klein, Dynamics of the Upper Oceanic Layers in Terms of Surface Quasigeostrophy Theory, Journal of Physical Oceanography, vol.36, issue.2, pp.165-176, 2006.
DOI : 10.1175/JPO2840.1

URL : https://hal.archives-ouvertes.fr/hal-00270025

L. Traon, P. Klein, P. Hua, B. Dibarboure, and G. , Do Altimeter Wavenumber Spectra Agree with the Interior or Surface Quasigeostrophic Theory?, Journal of Physical Oceanography, vol.38, issue.5, pp.1137-1142, 2008.
DOI : 10.1175/2007JPO3806.1

URL : https://hal.archives-ouvertes.fr/hal-00308932

L. Meur, O. Ebdelli, M. Guillemot, and C. , Hierarchical Super-Resolution-Based Inpainting, IEEE Transactions on Image Processing, vol.22, issue.10, pp.3779-3790, 2013.
DOI : 10.1109/TIP.2013.2261308

URL : https://hal.archives-ouvertes.fr/hal-00876168

R. Lguensat, P. Tandeo, R. Fablet, and R. Garello, Spatio-temporal interpolation of sea surface temperature using high resolution remote sensing data, 2014 Oceans, St. John's, 2014.
DOI : 10.1109/OCEANS.2014.7002988

URL : https://hal.archives-ouvertes.fr/hal-01188863

L. Lorenzi, F. Melgani, and G. Mercier, Inpainting Strategies for Reconstruction of Missing Data in VHR Images, IEEE Geoscience and Remote Sensing Letters, vol.8, issue.5, pp.914-918
DOI : 10.1109/LGRS.2011.2141112

K. Mccaffrey, B. Fox-kemper, and G. Forget, Estimates of ocean macro-turbulence: structure function and spectral slope from Argo profiling floats, J. Phys. Ocean, 2015.

S. Mallat, A Wavelet Tour of Signal Processing, 2008.

V. Nieves, C. Llebot, A. Turiel, J. Sole, E. Garcia-ladona et al., Common turbulent signature in sea surface temperature and chlorophyll maps, Geophysical Research Letters, vol.36, issue.3, p.34, 2007.
DOI : 10.1029/2007GL030823

J. D. Stark, C. J. Donlon, M. J. Martin, and M. E. Mcculloch, OSTIA : An operational, high resolution, real time, global sea surface temperature analysis system, OCEANS 2007, Europe, 2007.
DOI : 10.1109/OCEANSE.2007.4302251

G. Peyre, S. Bougleux, and L. Cohen, Non-local Regularization of Inverse Problems, Proc. Eur. Conference on Comp. Vis., ECCV'2008, pp.57-68, 2008.
DOI : 10.1007/978-3-540-88690-7_5

URL : https://hal.archives-ouvertes.fr/hal-00365030

Y. Romano, M. Protter, and M. Elad, Single Image Interpolation Via Adaptive Nonlocal Sparsity-Based Modeling, IEEE Transactions on Image Processing, vol.23, issue.7, pp.3085-3098, 2014.
DOI : 10.1109/TIP.2014.2325774

F. Rousseau, A non-local approach for image super-resolution using intermodality priors???, Medical Image Analysis, vol.14, issue.4, pp.594-605, 2010.
DOI : 10.1016/j.media.2010.04.005

URL : https://hal.archives-ouvertes.fr/hal-00440313

P. Tandeo, P. Ailliot, J. Ruiz, A. Hannart, B. Chapron et al., Combining Analog Method and Ensemble Data Assimilation: Application to the Lorenz-63 Chaotic System, Machine Learning and Data Mining Approaches to Climate Science, 2015.
DOI : 10.1007/978-3-319-17220-0_1

URL : https://hal.archives-ouvertes.fr/hal-01202496

Y. Xu and L. F. , Global Variability of the Wavenumber Spectrum of Oceanic Mesoscale Turbulence, Journal of Physical Oceanography, vol.41, issue.4, pp.802-809, 2011.
DOI : 10.1175/2010JPO4558.1

Z. Zhao and D. Giannakis, Analog forecasting with dynamics-adapted kernels. arXiv preprint arXiv:1412.3831, 2014 ANNEX We provide in this annex the detailed iterative algorithm used to solve for constrained minimization (15)). More precisely, we describe in the subsequent: ? Algorithm (1): the algorithm of function projection Interp LR which solves for the projection onto the interpolation and low-resolution constraints

@. Algorithm, ): the algorithm of function projection PSD PDF used to solve for the projection onto the spectral and marginal constraints (last two constraints in (16))