Abstract
Reconstruction of an image from a set of projections is a well‐established science, successfully exploited in X‐ray tomography and magnetic resonance imaging. This principle has been adapted to generate multidimensional NMR spectra, with the key difference that, instead of continuous density functions, high‐resolution NMR spectra comprise discrete features, relatively sparsely distributed in space. For this reason, a reliable reconstruction can be made from a small number of projections. This speeds the measurements by orders of magnitude compared to the traditional methodology, which explores all evolution space on a Cartesian grid, one step at a time. Speed is of crucial importance for structural investigations of biomolecules such as proteins and for the investigation of time‐dependent phenomena. Whereas the recording of a suitable set of projections is a straightforward process, the reconstruction stage can be more problematic. Several practical reconstruction schemes are explored. The deterministic methods—additive back‐projection and the lowest‐value algorithm—derive the multidimensional spectrum directly from the experimental projections. The statistical search methods include iterative least‐squares fitting, maximum entropy, and model‐fitting schemes based on Bayesian analysis, particularly the reversible‐jump Markov chain Monte Carlo procedure. These competing reconstruction schemes are tested on a set of six projections derived from the three‐dimensional 700‐MHz HNCO spectrum of a 187‐residue protein (HasA) and compared in terms of reliability, absence of artifacts, sensitivity to noise, and speed of computation. Copyright © 2006 John Wiley & Sons, Ltd.