Fast NMR Data Acquisition: Beyond the Fourier Transform
Chapter 6: Backprojection and Related Methods
Published:18 May 2017
Special Collection: 2017 ebook collectionSeries: New Developments in NMR
B. E. Coggins and P. Zhou, in Fast NMR Data Acquisition: Beyond the Fourier Transform, ed. M. Mobli and J. C. Hoch, The Royal Society of Chemistry, 2017, ch. 6, pp. 119-168.
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The sampling of the NMR time domain along radial spokes allows one to obtain projections of an NMR spectrum at various angles. These projections encode information about the positions, intensities, and lineshapes of the peaks in the spectrum, and this information can be recovered using suitable reconstruction methods. Here, we describe the technique of radial data collection and outline an intuitive framework for approaching reconstruction. We then survey the theory of tomographic reconstruction, and use that theory to analyze reconstruction methods and the information available from radial sampling. Finally, we survey past applications of projection–reconstruction methodology in NMR, including its use in 3-D and 4-D NMR data including NOESY.