Improved frequency resolution in multidimensional constant-time experiments by multidimensional Bayesian analysis.

The resolution of spectral frequencies in NMR data obtained from discrete Fourier transformation (DFT) along D constant-time dimensions can be improved significantly through extrapolation of the D-dimensional free induction decay (FID) by multidimensional Bayesian analysis. Starting from Bayesian probability theory for parameter estimation and model detection of one-dimensional time-domain data [Bretthorst, (1990) J. Magn. Reson., 88, 533-551; 552-570; 571-595], a theory for the D-dimensional case has been developed and implemented in an algorithm called BAMBAM (BAyesian Model Building Algorithm in Multidimensions). BAMBAM finds the most probable sinusoidal model to account for the systematic portion of any D-dimensional stationary FID. According to the parameters estimated by the algorithm, the FID is extrapolated in D dimensions prior to apodization and Fourier transformation. Multidimensional Bayesian analysis allows for the detection of signals not resolved by the DFT alone or even by sequential one-dimensional extrapolation from mirror-image linear prediction prior to the DFT. The procedure has been tested with a theoretical two-dimensional dataset and with four-dimensional HN(CO)CAHA (Kay et al. (1992) J. Magn. Reson., 98, 443-450) data from a small protein (8 kDa) where BAMBAM was applied to the 13C alpha and H alpha constant-time dimensions.