Fast multi-dimensional NMR acquisition and processing using the sparse FFT

Abstract

Increasing the dimensionality of NMR experiments strongly enhances the spectral resolution and provides invaluable direct information about atomic interactions. However, the price tag is high: long measurement times and heavy requirements on the computation power and data storage. We introduce Sparse Fast Fourier Transform (SFFT) as a new method of NMR signal collection and processing, which is capable of reconstructing high quality spectra of large size and dimensionality with short measurement times, faster computations than the Fast Fourier Transform, and minimal storage for processing and handling of sparse spectra. The new algorithm is described and demonstrated for a 4D BEST-HNCOCA spectrum.

Reconstruction of non-uniformly sampled five-dimensional NMR spectra by signal separation algorithm

“…The new reconstruction method outperforms the previously available SMFT, which employs bare nuFT. We would like to note that algorithms such as MDD (Orekhov and Jaravine 2011) or SFFT (Hassanieh et al 2015) are in principle also suitable for the processing of 5D NUS data, however, no implementation is so far available and thus one cannot compare the quality of reconstructions in terms of sensitivity, convergence and sampling thresholds. While α-synuclein used in this study is a relatively small IDP and thus spectral overlap is quite limited and possible to overcome using 3D and 4D spectroscopy, larger IDPs obviously exhibit more severe spectral crowding, which necessitates the acquisition of 5D experiments.…”

“…An essential technique to record four (and higher) dimensional spectra in reasonable experimental time is non-uniform sampling (NUS) (Nowakowski et al 2015). A particularly successful approach is randomized sparse sampling which enables robust reconstruction of high-resolution 3D–4D spectra from a tiny fraction of data points compared to uniform sampling (Mobli and Hoch 2008; Coggins et al 2010; Freeman and Kupče 2012; Hiller and Wider 2012; Kazimierczuk et al 2012; Hassanieh et al 2015). …”

XLSY: Extra‐Large NMR Spectroscopy

“…Thef requency identification borrows part of the SFFT algorithm [6] forf inding as hort list of frequencies in the spectrum that may have significant (that is,higher than noise) intensities.T his part is based on the radial sampling and the Fourier projection theorem. [7] Fora ni llustration of the algorithm, let us consider the simplest case of only two spectral dimensions each spanning Npoints.T he two-dimensional spectrum contains N N points with frequencyc oordinates (f 1 ,f 2 ).…”

Absolute Minimal Sampling in High‐Dimensional NMR Spectroscopy

“…The two sampling schemes can also be combined for the high-grade reconstruction of multidimensional spectra. [10] …”

“…Thet wo sampling schemes can also be combined for the high-grade reconstruction of multidimensional spectra. [10] Another approach is time-domain fitting,which was used originally in linear prediction (LP) in which atruncated timedomain signal is extended in time so that it can be subjected to regular Fourier transformation. [11] Although this improves spectral resolution and minimizes truncation artifacts,i ti s typically limited to atwo-fold reduction in measurement time per indirect dimension.…”