Spectral reconstruction methods in fast NMR: Reduced dimensionality, random sampling and maximum entropy

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The need to reduce data acquisition times of multidimensional NMR experiments has fostered considerable interest in novel data acquisition schemes. A recurring theme is that of reduced dimensionality experiments, in which time evolutions in the indirect dimensions are incremented together, rather than independently. Spectral analysis of such data is carried out using methods such as filtered back-projection, GFT, or parametric signal modeling. By using Maximum Entropy reconstruction of reduced-dimensionality data, we show that the artifacts that arise in reduced dimensionality experiments are intrinsic to the data sampling, and are not, in general, the result of the methods used to compute spectra. Our results illustrate that reduced dimensionality is a special case of non-uniform sampling in the time domain. We show that MaxEnt reconstruction yields more accurate spectra for reduced dimensionality data than back-projection reconstruction and that randomly choosing time increments based on an exponentially weighted distribution is more efficient, with fewer artifacts, than the systematic coupling of time increments used in most reduced dimensionality approaches.