E. O. Stejskal and J. E. Tanner, Spin Diffusion Measurements: Spin Echoes in the Presence of a Time???Dependent Field Gradient, The Journal of Chemical Physics, vol.42, issue.1, pp.288-292, 1965.
DOI : 10.1063/1.1695690

D. Sinnaeve, Concepts in Magnetic Resonance Part A, pp.39-65, 2012.

C. Johnson, Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications, Progress in Nuclear Magnetic Resonance Spectroscopy, vol.34, issue.3-4, pp.203-256, 1999.
DOI : 10.1016/S0079-6565(99)00003-5

W. S. Price, NMR Studies of Translational Motion: Principles and Applications, 2009.
DOI : 10.1017/CBO9780511770487

P. T. Callaghan, Translational dynamics and magnetic resonance: principles of pulsed gradient spin echo NMR, 2011.
DOI : 10.1093/acprof:oso/9780199556984.001.0001

P. Stilbs, K. Paulsen, and P. Griffiths, Global Least-Squares Analysis of Large, Correlated Spectral Data Sets:?? Application to Component-Resolved FT-PGSE NMR Spectroscopy, The Journal of Physical Chemistry, vol.100, issue.20, pp.8180-8189, 1996.
DOI : 10.1021/jp9535607

L. Van-gorkom and T. Hancewicz, Analysis of DOSY and GPC-NMR Experiments on Polymers by Multivariate Curve Resolution, Journal of Magnetic Resonance, vol.130, issue.1, pp.125-130, 1998.
DOI : 10.1006/jmre.1997.1292

W. Windig and B. Antalek, Direct exponential curve resolution algorithm (DECRA): A novel application of the generalized rank annihilation method for a single spectral mixture data set with exponentially decaying contribution profiles, Chemometrics and Intelligent Laboratory Systems, vol.37, issue.2, pp.241-254, 1997.
DOI : 10.1016/S0169-7439(97)00028-2

G. Armstrong, N. Loening, J. Curtis, A. Shaka, and V. Mandelshtam, Processing DOSY spectra using the regularized resolvent transform, Journal of Magnetic Resonance, vol.163, issue.1, pp.139-148, 2003.
DOI : 10.1016/S1090-7807(03)00126-5

R. Huo, R. Wehrens, and L. Buydens, Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting, Journal of Magnetic Resonance, vol.169, issue.2, pp.257-269, 2004.
DOI : 10.1016/j.jmr.2004.04.019

M. Nilsson and G. Morris, Speedy Component Resolution: An Improved Tool for Processing Diffusion-Ordered Spectroscopy Data, Analytical Chemistry, vol.80, issue.10, pp.3777-3782, 2008.
DOI : 10.1021/ac7025833

P. Stilbs, RECORD processing ??? A robust pathway to component-resolved HR-PGSE NMR diffusometry, Journal of Magnetic Resonance, vol.207, issue.2, pp.332-336, 2010.
DOI : 10.1016/j.jmr.2010.09.019

B. R. Martini, V. A. Mandelshtam, G. A. Morris, A. A. Colbourne, and M. Nilsson, Filter diagonalization method for processing PFG NMR data, Journal of Magnetic Resonance, vol.234, pp.125-134, 2013.
DOI : 10.1016/j.jmr.2013.06.014
URL : https://www.escholar.manchester.ac.uk/api/datastream?publicationPid=uk-ac-man-scw:205945&datastreamId=POST-PEER-REVIEW-NON-PUBLISHERS.PDF

D. Nuzillard, S. Bourgand, and J. Nuzillard, Model-Free Analysis of Mixtures by NMR Using Blind Source Separation, Journal of Magnetic Resonance, vol.133, issue.2, pp.358-363, 1998.
DOI : 10.1006/jmre.1998.1481

W. Naanaa and J. Nuzillard, Blind source separation of positive and partially correlated data, Signal Processing, vol.85, issue.9, pp.1711-1722, 2005.
DOI : 10.1016/j.sigpro.2005.03.006

A. Colbourne, G. Morris, and M. Nilsson, Local Covariance Order Diffusion-Ordered Spectroscopy: A Powerful Tool for Mixture Analysis, Journal of the American Chemical Society, vol.133, issue.20, pp.7640-7643, 2011.
DOI : 10.1021/ja2004895

I. Toumi, B. Torrésani, and S. Caldarelli, Effective Processing of Pulse Field Gradient NMR of Mixtures by Blind Source Separation, Analytical Chemistry, vol.85, issue.23, pp.11344-11351, 2013.
DOI : 10.1021/ac402085x
URL : https://hal.archives-ouvertes.fr/hal-00933934

J. Viéville, M. Tanty, and M. Delsuc, Polydispersity index of polymers revealed by DOSY NMR, Journal of Magnetic Resonance, vol.212, issue.1, pp.169-173, 2011.
DOI : 10.1016/j.jmr.2011.06.020

N. H. Williamson, M. Nydén, and M. Röding, The lognormal and gamma distribution models for estimating molecular weight distributions of polymers using PGSE NMR, Journal of Magnetic Resonance, vol.267, pp.54-62, 2016.
DOI : 10.1016/j.jmr.2016.04.007

S. W. Provencher, A constrained regularization method for inverting data represented by linear algebraic or integral equations, Computer Physics Communications, vol.27, issue.3, pp.213-227, 1982.
DOI : 10.1016/0010-4655(82)90173-4

M. Delsuc and T. E. Malliavin, Maximum Entropy Processing of DOSY NMR Spectra, Analytical Chemistry, vol.70, issue.10, pp.2146-2148, 1998.
DOI : 10.1021/ac9800715

M. Urba´nczykurba´nczyk, D. Bernin, W. Kozminski, and K. Kazimierczuk, Iterative Thresholding Algorithm for Multiexponential Decay Applied to PGSE NMR Data, Analytical Chemistry, vol.85, issue.3, pp.1828-1833, 2013.
DOI : 10.1021/ac3032004

M. Urba´nczykurba´nczyk, D. Bernin, A. Czuro´nczuro´n, and K. Kazimierczuk, Monitoring polydispersity by NMR diffusometry with tailored norm regularisation and moving-frame processing, The Analyst, vol.271, issue.5, pp.1745-1752, 2016.
DOI : 10.1039/C5AN02304A

K. Kazimierczuk, V. Orekhov, and . Yu, Accelerated NMR Spectroscopy by Using Compressed Sensing, Angewandte Chemie International Edition, vol.204, issue.24, pp.5556-5559, 2011.
DOI : 10.1002/anie.201100370

K. Xu and S. Zhang, Trust-Region Algorithm for the Inversion of Molecular Diffusion NMR Data, Analytical Chemistry, vol.86, issue.1, pp.592-599, 2013.
DOI : 10.1021/ac402698h

M. Elad, Sparse and Redundant Representations, 2010.
DOI : 10.1007/978-1-4419-7011-4
URL : https://hal.archives-ouvertes.fr/inria-00568893

H. H. Bauschke and P. L. Combettes, Convex analysis and monotone operator theory in Hilbert spaces, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00643354

R. M. Corless, G. H. Gonnet, D. E. Hare, D. J. Jeffrey, and D. E. Knuth, On the LambertW function, Advances in Computational Mathematics, vol.1, issue.6, pp.329-359, 1996.
DOI : 10.1007/BF02124750

N. Pustelnik, C. Chaux, and J. Pesquet, Parallel Proximal Algorithm for Image Restoration Using Hybrid Regularization, IEEE Transactions on Image Processing, vol.20, issue.9, pp.2450-2462, 2011.
DOI : 10.1109/TIP.2011.2128335
URL : https://hal.archives-ouvertes.fr/hal-00826121

P. L. Combettes and J. Pesquet, Inverse problems, pp.564-574, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00692901

P. L. Combettes, J. Pesquet, and I. J. Sel, A Douglas???Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery, IEEE Journal of Selected Topics in Signal Processing, vol.1, issue.4, pp.564-574, 2007.
DOI : 10.1109/JSTSP.2007.910264
URL : https://hal.archives-ouvertes.fr/hal-00621820

A. Jerschow and N. Müller, Suppression of Convection Artifacts in Stimulated-Echo Diffusion Experiments. Double-Stimulated-Echo Experiments, Journal of Magnetic Resonance, vol.125, issue.2, pp.372-375, 1997.
DOI : 10.1006/jmre.1997.1123

O. Assemat, M. Coutouly, R. Hajjar, and M. Delsuc, Validation of molecular mass measurements by means of diffusion-ordered NMR spectroscopy: Application to oligosaccharides, Comptes Rendus Chimie, vol.13, issue.4, pp.412-415, 2010.
DOI : 10.1016/j.crci.2009.10.005

R. Novoa-carballal, E. Fernandez-megia, C. Jimenez, and R. Riguera, NMR methods for unravelling the spectra of complex mixtures, Nat. Prod. Rep., vol.48, issue.1, pp.78-98, 2011.
DOI : 10.1039/C005320C

E. Chouzenoux, S. Moussaoui, J. Idier, and F. Mariette, Efficient Maximum Entropy Reconstruction of Nuclear Magnetic Resonance T1-T2 Spectra, IEEE Transactions on Signal Processing, vol.58, issue.12, pp.6040-6051, 2010.
DOI : 10.1109/TSP.2010.2071870
URL : https://hal.archives-ouvertes.fr/hal-00455477

E. Jaynes, Probability Theory: The Logic of Science, 2003.
DOI : 10.1017/CBO9780511790423