Concepts in Projection-Reconstruction

  • Ray FreemanEmail author
  • Ēriks Kupče
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 316)


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.


Bayesian Correlation Deterministic Hyperdimensional Multidimensional Nuclear magnetic resonance Projection-reconstruction Sparse sampling 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Jesus CollegeCambridge UniversityCambridgeUK
  2. 2.Agilent TechnologiesOxfordUK

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