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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%.

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Data availability

Example processing and analysis scripts and data will be available via the NMRPipe web site:

Software availability

The work makes use of the following software, which is all also available on the NMRbox cloud computing platform: NMRbox:, NMRPipe:, SMILE:, hmsIST: (download by request).









Discrete Fourier transform


Free induction decay


Iterative soft thresholding reconstruction




Nuclear magnetic resonance spectroscopy


Non-uniformly sampled


Radio frequency


Sparse multidimensional iterative line shape enhanced reconstruction


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This work was supported by start-up funds from Brown University and funds from the COBRE Center for Computational Biology of Human Disease (NIH P20-GM109035).


Certain commercial equipment, instruments, and materials are identified in this presentation in order to specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the material or equipment identified is necessarily the best available for the purpose.

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Correspondence to George P. Lisi.

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East, K.W., Delaglio, F. & Lisi, G.P. A simple approach for reconstruction of non-uniformly sampled pseudo-3D NMR data for accurate measurement of spin relaxation parameters. J Biomol NMR 75, 213–219 (2021).

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  • Non-uniform sampling
  • Spin relaxation
  • Spectral reconstruction