No Dice

Magnetic resonance is a powerful tool for interrogating materials at the atomic level, whether in determining protein structures or imaging the body. The procedure entails measuring the dynamics of the magnetism after it has been perturbed by radio waves. Usually the evolution is sampled at equal intervals, which is straightforward over one evolution period. However, experiments increasingly involve transfers of magnetization between different groups of atoms and require measurements after each transfer. In such experiments, it can become overwhelming to sample all the points in each evolution period, from the early ones needed because they have the strongest signal, to the late points needed because they provide the resolution of different contributions. Therefore, much recent attention has been given to finding ways to sample non-uniformly. This work led to a consensus that if one drops points it is necessary to do so randomly to minimize artifacts. The problem is that one can randomly get a very bad sampling schedule and waste a whole experiment (worse yet without necessarily knowing that the sampling schedule is the problem). Now, a MIT-Brandeis team1 has shown that non-uniform sampling need not be random and that adhering closely to a suitable distribution function produces high quality results.

1.      Eddy MT, Ruben D, Griffin RG and Herzfeld J*.  Deterministic schedules for robust and reproducible non-uniform sampling in multidimensional NMR, J. Magn. Reson. (2011), doi:10.1016/j.jmr.2011.12.002

An example of cumulative distribution functions (top) and results (bottom) for non-random sampling (right) compared with random sampling (left).

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