On Two Approaches to 3D Reconstruction in NMR Zeugmatography

In nuclear magnetic resonance (NMR) zeugmatography, the primary data pertain to integrals of the unknown nuclear spin density f(x,y,z) over planes instead of 1ines in R3. Two “natural” approaches to reconstructing f from such data are: (1) By numerical implementation of the inverse Radon transform in three dimensions (the direct approach), and (2) by application, in two successive stages, of existing well-known algorithms for inverting the two-dimensional Radon transform (the two-stage approach). These two approaches are discussed and compared, both from a theoretical standpoint and through computer results obtained with real NMR data. For the cases studied to date the two methods appear to produce qualitatively similar results.

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