Projective reconstruction

Some "fast methods" such as single-scan experiments,93 94 Hadamard95 and projection-reconstruction techniques96 take a few seconds to produce 2D spectra, but suffer from a lack of spectral resolution. As mentioned... 

Building High-Resolution Spectra Using Projection-Reconstruction Techniques... 

Vosegaard and Massiot [144] showed that it is possible to create a high-resolution 2D spectrum correlating the chemical shifts with the second-order quadrupolar lineshapes from several spectra recorded at different magnetic field strengths using a projection-reconstruction method called chemical shift-quadrupolar projection-reconstruction of one-dimensional spectra (CQ-PRODI). 

One-dimensional images of toluic acid were obtained with a stationary sample. For two-dimensional images, the 4-bromobenzoic acid crystal was rotated about an axis orthogonal to the gradient direction in constant increments of either 3° or 6° over a range of 180° to collect sets of 60 or 30 one-dimensional projections, respectively. The two-dimensional images were calculated with the filtered back-projection reconstruction algorithm (36). 

A third area of development that has affected the speed of obtaining molecular connectivity information from NMR takes advantage of the information inherently present in two separate experiments. Traditionally, an analyst would use the information from a group of separate experiments to draw conclusions about molecular connectivity. In recent years, the projection-reconstruction technique97,98 and indirect covariance NMR99 have allowed information from two separately acquired experiments to be correlated into an additional experiment. Both techniques can increase the dimensionality of NMR data providing information that would otherwise require time-consuming acquisitions. 

The projection-reconstruction approach is a technique unrelated to covariance processing which can provide data typically inaccessible to the natural product chemist. For example, 13C-15N correlation spectra were obtained for vitamin B12 at natural abundance.104 Compared with a conventional three-dimensional 13C-15N correlation experiment, the projection-reconstruction method provides a sensitivity enhancement of two orders of magnitude. The final 13C-15N spectrum was reconstructed from data obtained from ll l5N and H- C correlations acquired using a time-shared evolution pulse sequence that allowed all the information to be obtained in one experiment.104 Martin and co-workers also demonstrated the ability to generate 13C-15N correlation spectra using unsymmetrical indirect covariance NMR with vinblastine as an example.105 In the latter case, 13C-15N correlation spectra were obtained from - C HSQC data and H-1sN HMBC data that were acquired separately. Both methods provide access to correlations that would be inaccessible for most natural products at natural abundance. 

Fig. 3 Transaxial slices reconstructed with filtered back projection (top row) and iterative reconstruction (bottom row). Negative reconstructed values have been set to zero for the filtered back projection reconstruction. The streak artifacts and count defects caused by focal activity deposition in the central airways are clearly evident on the reconstructions with filtered back projection. The iterative reconstruction provides artifact free images.

X. Zhou and P. C. Lauterbur, NMR microscopy using projection reconstruction, inMagnetic Resonance Microscopy B. Blumich and W. Kuhn, eds., VCH Publishers, New York, 1992, 3. 

Ramanathan and Ackerman (1999) have shown that solid-state 31P NMR imaging can be used to measure quantitatively the mass of hydroxyapatite in the presence of bone hence to follow non-invasively the resorption and remodeling of calcium phosphate implants in vivo. A three-dimensional projection reconstruction technique has been used to record NMR images in the presence of a fixed amplitude field gradient, the direction of which was varied uniformly over the unit sphere. Chemical selection was achieved using differences in T1 relaxation time of neighbouring protons as the synthetic hydroxyapatite has a shorter T1 (1.8 s at 4.7 T) compared to bone (approximately 15 s at 4.7 T in vivo, 42 s ex vivo). The experimental results demonstrated that a linear relationship exists between image intensity and HAp density. 

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

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