title: Concepts in projection-reconstruction.
abstract: The Achilles heel of conventional multidimensional NMR spectroscopy is the long duration of the measurements, set by the Nyquist sampling condition and the resolution requirements in the evolution dimensions. Projection-reconstruction solves this problem by radial sampling of the evolution-domain signals, relying on Bracewell's Fourier transform slice/projection theorem to generate a set of projections at different inclinations. Reconstruction is implemented by one of three possible deterministic back-projection schemes (additive, lowest-value, or algebraic), or by a statistical model-fitting program. For simplicity the treatment focuses principally on the three-dimensional case, and then extends the analysis to four dimensions. The concept of hyperdimensional spectroscopy is described for dealing with even higher dimensions.
authors.affiliation: Jesus College, Cambridge University, Cambridge, UK. rf110@hermes.cam.ac.uk
authors.forename: Ray
authors.initials: R
authors.lastname: Freeman
authors.forename: Ēriks
authors.initials: Ē
authors.lastname: Kupče
mesh_terms: D000465:Algorithms; D009682:Magnetic Resonance Spectroscopy / Q000592:standards; D012015:Reference Standards