A simple approach for reconstruction of non-uniformly sampled pseudo-3D NMR data for accurate measurement of spin relaxation parameters

We explain how to conduct a pseudo-3D relaxation series NUS measurement so that it can be reconstructed by existing 3D NUS reconstruction methods to give accurate relaxation values. We demonstrate using reconstruction algorithms IST and SMILE that this 3D approach allows lower sampling densities than for independent 2D reconstructions. This is in keeping with the common finding that higher dimensionality increases signal sparsity, enabling lower sampling density. The approach treats the relaxation series as ordinary 3D time-domain data whose imaginary part in the pseudo-dimension is zero, and applies any suitably linear 3D NUS reconstruction method accordingly. Best results on measured and simulated data were achieved using acquisitions with 9 to 12 planes and exponential spacing in the pseudo-dimension out to ~ 2 times the inverse decay time. Given these criteria, in typical cases where 2D reconstructions require 50% sampling, the new 3D approach generates spectra reliably at sampling densities of 25%.