Optimizing resolution in multidimensional NMR by three-way decomposition

Resolution depends on the number of points sampled in a FID; in indirectly detected dimensions it is an important determinant of the total experiment time. Based on the high redundancy present in NMR data, we propose the following timesaving scheme for three-dimensional spectra. An extensive grid of discrete t1- and t2-values is used, which increases resolution while preserving the spectral width. Total experiment time is reduced by avoiding the recording of t3-FIDs for selected pairs of t1 and t2; typically the recording is omitted for about 75% of the (t1,t2) combinations. These data sets are referred to as sparse, and post-experimental processing making optimal use of spectral redundancy provides the missing, non-recorded data. We have previously shown that three-way decomposition (TWD) within the MUNIN approach provides a practical way to process dense NMR data sets. Here, a novel TWD algorithm [Ibraghimov, (2002) Numer. Linear Algebra Appl.9, 551–565] is used to complement a sparselyrecorded time-domain data set by providing the missing FIDs for all (t1,t2) combinations omitted in the experiment. A necessary condition is that for each t1-value at least a few FIDs are recorded, and similar for each t2-value. The method is demonstrated on non-uniformly sampled ¹⁵N-NOESY-HSQC data sets recorded for the 14 kD protein azurin. The spectra obtained by TWD, reconstruction and ordinary transform to frequency-domain are, in spite of the large number of signals and the high dynamic range typical for NOESYs, highly similar to a corresponding reference spectrum, for which all (t1,t2) combinations were recorded.