Using Deep Neural Networks to Reconstruct Non-uniformly Sampled NMR Spectra

D Flemming Hansen

doi:10.1007/s10858-019-00265-1

Abstract

Non-uniform and sparse sampling of multi-dimensional NMR spectra has over the last decade become an important tool to allow for fast acquisition of multi-dimensional NMR spectra with high resolution. The success of non-uniform sampling NMR hinge on both the development of algorithms to accurately reconstruct the sparsely sampled spectra and the design of sampling schedules that maximise the information contained in the sampled data. Traditionally, the reconstruction tools and algorithms have aimed at reconstructing the full spectrum and thus ‘fill out the missing points’ in the time-domain spectrum, although other techniques are based on multi-dimensional decomposition and extraction of multi-dimensional shapes. Also over the last decade, machine learning, deep neural networks, and artificial intelligence have seen new applications in an enormous range of sciences, including analysis of MRI spectra. As a proof-of-principle, it is shown here that simple deep neural networks can be trained to reconstruct sparsely sampled NMR spectra. For the reconstruction of two-dimensional NMR spectra, reconstruction using a deep neural network performs as well, if not better than, the currently and widely used techniques. It is therefore anticipated that deep neural networks provide a very valuable tool for the reconstruction of sparsely sampled NMR spectra in the future to come.

Highlights

Reconstruction of non-uniformly sampled (NUS) NMR spectra has become a very important tool for obtaining ultra-high dimensional NMR spectra with high resolution and in a short time
Being able to accurately reconstruct NUS NMR spectra allows for high-resolution four-dimensional methyl–methyl NOESY spectra for chemical shift assignment and characterisations of large proteins (Tugarinov et al 2005; Vuister et al 1993; Hyberts et al 2012), five-dimensional spectral of intrinsically disordered proteins for chemical shift assignments (Krähenbühl et al 2012; Kosiński et al 2017), and fast characterisation
Sparse sampling of NMR spectra is possible because the information contained in the spectrum is often far less than the actual number of data points sampled on the full Nyquist grid

Summary

Introduction

Reconstruction of non-uniformly sampled (NUS) NMR spectra has become a very important tool for obtaining ultra-high dimensional NMR spectra with high resolution and in a short time. Various algorithms have been developed to reconstruct the full dataset from the sparsely sampled data (Hyberts et al 2012; Ying et al 2017; Coggins et al 2012; Orekhov and Jaravine 2011; Balsgart and Vosegaard 2012; Holland et al 2011; Kazimierczuk and Orekhov 2011), or otherwise extract NMR parameters from the dataset (Eghbalnia et al 2005; Murrali et al 2018; Dutta et al 2015; Pustovalova et al 2018). It has become clear that it is the algorithm used to process the sparse data that determines the accuracy with which information can be obtained from NUS NMR data, since the sampling schedule used has a substantial impact on the final outcome (Hyberts et al 2012). Traditional applications of DNN include image processing and speech recognition, whereas applications involving the analysis of EPR DEER spectra (Worswick et al 2018) and reconstruction of MRI (Han and Ye 2018; Hyun et al. Vol.:(0123456789)

Methods

Results

Conclusion