Quantitative porosity profiles and wettability contrast visualisation in sandstone by CPMG imaging

Extrapolation and phase correction of non-uniformly broadened signals

The initial part of FID-signals cannot always be acquired experimentally. This is particularly true for signals characterised by strong inhomogeneous broadening, such as those in porous materials, e.g. cements, soils and rocks, those measured by portable NMR-apparatus, or EPR-signals. Here we report on a numerical method we designed to extrapolate those initial missing parts, i.e. to retrieve their amplitude and phase. Should the entire signal be available from an experiment, the algorithm can still be used as an automatic phase-corrector and a low-pass filter. The method is based on the use of cardinal series, applies to any oversampled signals and requires no prior knowledge of the system under study. We show that the method can also be used to restore entire one-dimensional MRI-data sets from those in which less than half of the k-space was sampled, thus not only potentially allowing to speed up data acquisition - when extended to two or three dimensions, but also to circumvent phase-distortions usually encountered when exploring the k-space near its origin.

Cardinal series to restore NMR-signals dominated by strong inhomogeneous broadening

We have devised two numerical methods of restoring incomplete band-limited NMR-signals to integrity by either interpolating or extrapolating them. Both methods are based on use of the finite cardinal series, whose filtering properties were discussed previously, to model signals. They require no prior knowledge about the system under study, but only that the available parts of the signal were oversampled enough. The methods were tested on two types of computer-simulated signal. It proved superior to the linear prediction methods and Lagrange interpolation when applied to signals measured in highly inhomogeneous magnetic fields. The extrapolation method was then applied to restore experimentally-measured refocused FID-signals of a porous medium. The missing parts of the signal of up to several times the size of its Nyquist period could be recovered by either method.