High-throughput Nuclear Magnetic Resonance (NMR) spectroscopy, as well as structural determination of biomolecules and characterization of short-lived molecular systems by multi-dimensional NMR spectroscopy require to shorten the data measurement time, meanwhile to achieve higher resolution and sensitivity NMR spectra. Currently proposed Non-uniform Sampling (NUS) scheme provides an ingenious way to accomplish the abovementioned goals. In this thesis work, I analyzed and modified two NUS spectral reconstruction schemes and demonstrated they are more robust than the previously described methods.

At first, high-resolution NMR spectral reconstruction method, constrained Hankel nuclear norm minimization algorithm (CHARM), is proposed, which outperforms the Hankel nuclear norm minim...[ Read more ]

High-throughput Nuclear Magnetic Resonance (NMR) spectroscopy, as well as structural determination of biomolecules and characterization of short-lived molecular systems by multi-dimensional NMR spectroscopy require to shorten the data measurement time, meanwhile to achieve higher resolution and sensitivity NMR spectra. Currently proposed Non-uniform Sampling (NUS) scheme provides an ingenious way to accomplish the abovementioned goals. In this thesis work, I analyzed and modified two NUS spectral reconstruction schemes and demonstrated they are more robust than the previously described methods.

At first, high-resolution NMR spectral reconstruction method, constrained Hankel nuclear norm minimization algorithm (CHARM), is proposed, which outperforms the Hankel nuclear norm minimization algorithm (HARM) method showing higher resolution and sensitivity.

Secondly, super-resolution NMR spectral reconstruction method named zero constrained Toeplitz minimization (zc-TOP) is put forward, in which through minimizing the trace of a Toeplitz matrix formed by the NUS data set to recover the unrecorded data points computationally. In addition, the decay function is extracted by fitting to the limited number of NUS data points. After applying the decay function into the minimization and deconvolution procedures, the non-decayed free induction data (FID) is used to reconstruct a super-resolution NMR spectrum.

Moreover, the NUS sampling scheme is also analyzed as different sampling schemes will result in different reconstruction spectra. According to our results, the exponential sampling scheme among the first half of the FID for decay signals and among the whole FID for non-decay signals show better spectral reconstruction results for our proposed methods.

To achieve higher resolution NMR spectra by post-processing solvent suppression scheme, a singular value decomposition (SVD) based solvent suppression algorithm is developed to extract the useful information buried by the extremely strong solvent signal. The FID is decomposed first and then singular values represent the solvent information are set to zeros. Consequently, the undesired solvent signal is removed.

With the above methods, we were able to obtain NMR spectra with high resolution, sensitivity and less experimental time. We believed that these methods could be widely used in the NMR community.