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NMR is a tool of choice for the measure of diffusion coefficients of speciesin solution. The DOSY experiment, a 2D implementation of this measure, hasproven to be particularly useful for the study of complex mixtures, molecularinteractions, polymers, etc. However, DOSY data analysis requires to resort toinverse Laplace transform, in particular for polydisperse samples. This is aknown difficult numerical task, for which we present here a novel approach. Anew algorithm based on a splitting scheme and on the use of proximity operatorsis introduced. Used in conjunction with a Maximum Entropy and $\ell_1$ hybridregularisation, this algorithm converges rapidly and produces results robustagainst experimental noise. This method has been called PALMA. It is able toreproduce faithfully monodisperse as well as polydisperse systems, and numeroussimulated and experimental examples are presented. It has been implemented onthe server http://palma.labo.igbmc.fr where users can have their datasetsprocessed automatically.

PALMA, an improved algorithm for DOSY signal processing