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Two dimensional nuclear magnetic resonance (NMR) spectroscopy is one of themajor tools for analysing the chemical structure of organic molecules andproteins. Despite its power, this technique requires long measurement times,which, particularly in the recently emerging diamond based single molecule NMR,limits its application to stable samples. Here we demonstrate a method whichallows to obtain the spectrum by collecting only a small fraction of theexperimental data. Our method is based on matrix completion which can recoverthe full spectral information from randomly sampled data points. We confirmexperimentally the applicability of this technique by performing twodimensional electron spin echo envelope modulation (ESEEM) experiments on a twospin system consisting of a single nitrogen vacancy (NV) centre in diamondcoupled to a single 13C nuclear spin. We show that the main peaks in thespectrum can be obtained with only 10 % of the total number of the data points.We believe that our results reported here can find an application in all typesof two dimensional spectroscopy, as long as the measured matrices have a lowrank.

Accelerated 2D magnetic resonance spectroscopy of single spins using matrix completion