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Concepts in Projection-Reconstruction

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Novel Sampling Approaches in Higher Dimensional NMR

Part of the book series: Topics in Current Chemistry ((TOPCURRCHEM,volume 316))

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.

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Author information

Authors and Affiliations

  1. Jesus College, Cambridge University, Cambridge, UK

    Ray Freeman

  2. Agilent Technologies, 6 Mead Road, Yarnton, Oxford, UK

    Ēriks Kupče

Authors
  1. Ray Freeman
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  2. Ēriks Kupče
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Corresponding author

Correspondence to Ray Freeman .

Editor information

Editors and Affiliations

  1. , Department of Chemistry, University of Gothenburg, Göteborg, 405 30, Sweden

    Martin Billeter

  2. , The Swedish NMR Centre, Göteborg University, Medicinaregatan 5C, Göteborg, 413 90, Sweden

    Vladislav Orekhov

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Freeman, R., Kupče, Ē. (2010). Concepts in Projection-Reconstruction. In: Billeter, M., Orekhov, V. (eds) Novel Sampling Approaches in Higher Dimensional NMR. Topics in Current Chemistry, vol 316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/128_2010_103

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